If `sin theta+ sin^2theta+ sin^3theta=1` ,prove that `cos^6theta-4 cos^4theta+8cos^2= 4`

If `sin theta+ sin^2theta+ sin^3theta=1` ,prove that `cos^6theta-4 cos^4theta+8cos^2= 4`
by

1 Answer

Answer :

If `sin theta+ sin^2theta+ sin^3theta=1` ,prove that `cos^6theta-4 cos^4theta+8cos^2= 4`
by

Related questions

The sum of all values of `theta in (0,pi/2)` satisfying `sin^(2)2theta+cos^(4)2theta=3/4` is

Description : The sum of all values of `theta in (0,pi/2)` satisfying `sin^(2)2theta+cos^(4)2theta=3/4` is

Last Answer : The sum of all values of `theta in (0,pi/2)` satisfying `sin^(2)2theta+cos^(4)2theta=3/4` is A. `pi` B. `(pi)/(2)` C. `(3pi)/(8)` D. `(5pi)/(4)`

The equation `2sin^3theta+(2lambda-3)sin^2theta-(3lambda+2)sintheta-2lambda=0` has exactly three roots in `(0,2pi)` , then `lambda` can be equal to 0

Description : The equation `2sin^3theta+(2lambda-3)sin^2theta-(3lambda+2)sintheta-2lambda=0` has exactly three roots in `(0,2pi)` , then `lambda` can be equal to 0

Last Answer : The equation `2sin^3theta+(2lambda-3)sin^2theta-(3lambda+2)sintheta-2lambda=0` has exactly three roots in `(0,2pi)` , ... -1 B. 0 C. `(1)/(2)` D. 1

An isosceles triangle of vertical angle `2theta` is inscribed in a circle of radius `a` . Show that the area of the triangle is maximum when `theta=pi

Description : An isosceles triangle of vertical angle `2theta` is inscribed in a circle of radius `a` . Show that the area of the triangle is maximum when `theta=pi

Last Answer : An isosceles triangle of vertical angle `2theta` is inscribed in a circle of radius `a` . Show that the area of ... pi/4` C. `pi/6` D. None of these.

Find the equation of the tangent to the curve `x=theta+sin theta ,y=1+cos theta` at `theta=pi/4`

Description : Find the equation of the tangent to the curve `x=theta+sin theta ,y=1+cos theta` at `theta=pi/4`

Last Answer : Find the equation of the tangent to the curve `x=theta+sin theta ,y=1+cos theta` at `theta=pi/4` A. ` ... 1+sqrt2)x+(sqrt2-1) pi` D. None of the above

Let `theta ,phi in [0,2pi]` be such that `2 cos theta (1-sin phi)=sin^2 theta ((tan)theta/2+(cot)theta/2) cos phi -1, tan(2pi-theta) > 0 and -1 &lt

Description : Let `theta ,phi in [0,2pi]` be such that `2 cos theta (1-sin phi)=sin^2 theta ((tan)theta/2+(cot)theta/2) cos phi -1, tan(2pi-theta) > 0 and -1 <

Last Answer : Let `theta ,phi in [0,2pi]` be such that `2 cos theta (1-sin phi)=sin^2 theta ((tan)theta/2+(cot)theta/2) ... (3pi)/(2)` D. `(3pi)/(2) lt phi lt 2pi`

If a cos theta plus b sin theta equals 8 and a sin theta - b cos theta equals 5 show that a squared plus b squared equals 89?

Description : If a cos theta plus b sin theta equals 8 and a sin theta - b cos theta equals 5 show that a squared plus b squared equals 89?

Last Answer : There is a hint to how to solve this in what is required to be shown: a and b are both squared.Ifa cos θ + b sin θ = 8a sin θ - b cos θ = 5then square both sides of each to get:a² cos² θ + 2ab cos ... + sin² θ) + b² (sin² θ + cos² θ) = 89using cos² θ + sin² θ = 1â†' a² + b² = 89

If cos and theta 0.65 what is the value of sin and theta?

Description : If cos and theta 0.65 what is the value of sin and theta?

Last Answer : You can use the Pythagorean identity to solve this:(sin theta) squared + (cos theta) squared = 1.

Prove that (sin A + sin 3A + sin 5A + sin7 A)/(Cos A + Cos3 A + cos5 A + cos7 A) = tan 4A. -Maths 9th

Description : Prove that (sin A + sin 3A + sin 5A + sin7 A)/(Cos A + Cos3 A + cos5 A + cos7 A) = tan 4A. -Maths 9th

Last Answer : answer:

If cosec |-sin |=l and sec |- cos |=m, prove that l2m2(l2+m2+3)=1 -Maths 9th

Description : If cosec |-sin |=l and sec |- cos |=m, prove that l2m2(l2+m2+3)=1 -Maths 9th

Last Answer : cosec(A) - sin(A) = l ⇒ 1/sin(A) - sin(A) = l ⇒ l² = 1/sin²(A) + sin²(A) - 2 --------- sec(A) - cos(A) = m ⇒ 1/cos(A) - cos(A) = m ⇒ m² = 1/cos²(A) + cos²(A) - 2 ---------- l²m² = [1/sin²(A) + ... A)) = = 1/(sin²(A)cos²(A)) ------------- ⇒ l²m² (l² + m² + 3) = sin²(A)cos²(A) / [sin²(A)cos²(A)] = 1

If x sin3|+ y cos3|=sin|cos| and xsin|=ycos|, prove x2+y2=1. -Maths 9th

Description : If x sin3|+ y cos3|=sin|cos| and xsin|=ycos|, prove x2+y2=1. -Maths 9th

Last Answer : xsin3θ+ycos3θ=sinθcosθ (xsinθ)sin2θ+(ycosθ)cos2θ=sinθcosθ (xsinθ)sin2θ+(xsinθ)cos2θ=sinθcosθ xsinθ=sinθcosθ x=cosθ Again, ycosθ=xsinθ ycosθ=cosθsinθ y=sinθ Therefore, x2+y2=sin2θ+cos2θ=1.

Using the rule for differentiation for quotient of two functions, prove that d/dx (sin x/cos x) = sec^2 x

Description : Using the rule for differentiation for quotient of two functions, prove that d/dx (sin x/cos x) = sec^2 x

Last Answer : Using the rule for differentiation for quotient of two functions, prove that d/dx (sin x/cos x) = sec2x

If `2cosec theta - cos theta cot theta >= k AA theta in (0,pi),` then value of `k` is

Description : If `2cosec theta - cos theta cot theta >= k AA theta in (0,pi),` then value of `k` is

Last Answer : If `2cosec theta - cos theta cot theta >= k AA theta in (0,pi),` then value of `k` is

Let `0le theta le pi/2` `x=Xcos theta + Ysin theta` `y=Xsin theta - Y cos theta` such that `x^2+4xy+y^2=aX^2+bY^2` where `a,b` are constants such that

Description : Let `0le theta le pi/2` `x=Xcos theta + Ysin theta` `y=Xsin theta - Y cos theta` such that `x^2+4xy+y^2=aX^2+bY^2` where `a,b` are constants such that

Last Answer : Let `0le theta le pi/2` `x=Xcos theta + Ysin theta` `y=Xsin theta - Y cos theta` such that `x^2+4xy+y^2=aX^2+ ... C. `a=3`, `b=-1` D. `theta=(pi)/(3)`

What are both solutions between 0 degrees and 360 degrees of the equation cos theta 911?

Description : What are both solutions between 0 degrees and 360 degrees of the equation cos theta 911?

Last Answer : They are 35.1 and 324.9 degrees.

The maximum value of the expression `(1)/(sin^(2)theta+3sinthetacostheta+5cos^(2)theta)` is

Description : The maximum value of the expression `(1)/(sin^(2)theta+3sinthetacostheta+5cos^(2)theta)` is

Last Answer : The maximum value of the expression `(1)/(sin^(2)theta+3sinthetacostheta+5cos^(2)theta)` is

If sin theta equals 3/4 and theta is in quadrant II what is the value of tan theta?

Description : If sin theta equals 3/4 and theta is in quadrant II what is the value of tan theta?

Last Answer : 0.75

The set of angles between `0` and `2pi` satisfying the equation `4cos^2theta-2sqrt2costheta-1=0` is

Description : The set of angles between `0` and `2pi` satisfying the equation `4cos^2theta-2sqrt2costheta-1=0` is

Last Answer : The set of angles between `0` and `2pi` satisfying the equation `4cos^2theta-2sqrt2costheta-1=0` is A. `{(pi)/( ... (7pi)/(12),(17)/(12),(23pi)/(12)}`

Explaining the derivatives of sin, cos and toa?

Description : Explaining the derivatives of sin, cos and toa?

Last Answer : answer:I am assuming this isn't homework, as it is summer and from what you wrote it appears you are merely curious, so I think it's legal for me to do the proof here for you (don't strike me down, ... proof for that as well. By toa do you mean tangent? I can prove that one too if you'd like.

What's the key to remembering how to draw each of the different trigonometric function graphs? (i.e. sin, cos, tan)

Description : What's the key to remembering how to draw each of the different trigonometric function graphs? (i.e. sin, cos, tan)

Last Answer : SOH – sin CAH – cos TOA – tan sin = opposite over hypotenuse cos = adjacent over hypotenuse tan = opposite over adjacent

How to use sin, cos, and tan on a TI-84+Silver Edition?

Description : How to use sin, cos, and tan on a TI-84+Silver Edition?

Last Answer : answer:This may work, haven't tried a real problem yet . here are the steps in changing it from radian to degrees 1. turn on your TI-83 plus 2. press the MODE button near the top of your ... down to options and move the highlight from radian to degree, press enter and clear you're good to go

What is SIN, TAN, COS?

Description : What is SIN, TAN, COS?

Last Answer : Wikipedia knows.

Which of the following represents shearing? a.(x, y) → (x+shx, y+shy) b.(x, y) → (ax, by) c.(x, y) → (x cos(θ)+y sin(θ), -x sin(θ)+y cos(θ)) d.(x, y) → (x+shy, y+shx)

Description : Which of the following represents shearing? a.(x, y) → (x+shx, y+shy) b.(x, y) → (ax, by) c.(x, y) → (x cos(θ)+y sin(θ), -x sin(θ)+y cos(θ)) d.(x, y) → (x+shy, y+shx)

Last Answer : d.(x, y) → (x+shy, y+shx)

The original coordinates of the point in polar coordinates are a.X’=r cos (Ф +ϴ) and Y’=r cos (Ф +ϴ) b.X’=r cos (Ф +ϴ) and Y’=r sin (Ф +ϴ) c.X’=r cos (Ф -ϴ) and Y’=r cos (Ф -ϴ) d.X’=r cos (Ф +ϴ) and Y’=r sin (Ф -ϴ)

Description : The original coordinates of the point in polar coordinates are a.X’=r cos (Ф +ϴ) and Y’=r cos (Ф +ϴ) b.X’=r cos (Ф +ϴ) and Y’=r sin (Ф +ϴ) c.X’=r cos (Ф -ϴ) and Y’=r cos (Ф -ϴ) d.X’=r cos (Ф +ϴ) and Y’=r sin (Ф -ϴ)

Last Answer : b.X’=r cos (Ф +ϴ) and Y’=r sin (Ф +ϴ)

For any two real number a b and , we defined aRb if and only if sin^2a + cos^2b = 1. The relation R is -Maths 9th

Description : For any two real number a b and , we defined aRb if and only if sin^2a + cos^2b = 1. The relation R is -Maths 9th

Last Answer : (d) an equivalence relationGiven, a R b ⇒ sin2a + cos2b = 1 Reflexive: a R a ⇒ sin2 a + cos2 a = 1 ∀ a ∈ R (True) Symmetric: a R b ⇒ sin2 a + cos2 b = 1 ⇒ 1 - cos2 a + 1 - sin2 b = 1 ⇒ sin2 b + ... + cos2 b + sin2 b + cos2 c = 2 ⇒ sin2 a + cos2 c = 1 ⇒ a R c (True)∴ R is an equivalence relation.

If A lies in the third quadrant and 3 tan A – 4 = 0, then what is the value of 5 sin 2 A + 3 sin A + 4 cos A? -Maths 9th

Description : If A lies in the third quadrant and 3 tan A – 4 = 0, then what is the value of 5 sin 2 A + 3 sin A + 4 cos A? -Maths 9th

Last Answer : answer:

If tan x = b/a , then what is the value of a cos 2x + b sin 2x? -Maths 9th

Description : If tan x = b/a , then what is the value of a cos 2x + b sin 2x? -Maths 9th

Last Answer : answer:

The angle A lies in the third quadrant and it satisfies the equation 4 (sin^2x + cos x) = 1. What is the measure of angle A? -Maths 9th

Description : The angle A lies in the third quadrant and it satisfies the equation 4 (sin^2x + cos x) = 1. What is the measure of angle A? -Maths 9th

Last Answer : answer:

If cosec A = 2, then the value of 1/(tan A) + (sin A)/(1+cos A) is -Maths 9th

Description : If cosec A = 2, then the value of 1/(tan A) + (sin A)/(1+cos A) is -Maths 9th

Last Answer : answer:

What is the value of sin A cos A tan A + cos A sin A cot A ? -Maths 9th

Description : What is the value of sin A cos A tan A + cos A sin A cot A ? -Maths 9th

Last Answer : answer:

sin ^ 2 θ = cos ^ 2 θ = 1 How is it ?

Last Answer : We hold theta = A. sin2A + cos2 (PM / OP) 2+ (OM / OP) 2 PM2 / OP2 + OM2OP2 (PM2 + OM2) / OP2 OP2 / OP2 => 1 So sin2A + cos2A = 1

`int_(0)^(pi//2) (sin x -cos x)/(1+sin x cos x) dx=?`

Description : `int_(0)^(pi//2) (sin x -cos x)/(1+sin x cos x) dx=?`

Last Answer : `int_(0)^(pi//2) (sin x -cos x)/(1+sin x cos x) dx=?` A. `0` B. `1` C. None of the above D.

`int (1)/(sqrt(sin^(3) x cos x))dx =?`

Description : `int (1)/(sqrt(sin^(3) x cos x))dx =?`

Last Answer : `int (1)/(sqrt(sin^(3) x cos x))dx =?` A. `-2sqrt(tan x) +c` B. `(2)/(sqrt(tan x)) +c` C. `(-2)/(sqrt(tan x)) +c` D.

`" if " int (sin 2x- cos 2x) dx=(1)/(sqrt(2)) sin (2x-k)+c " then " k=?`

Description : `" if " int (sin 2x- cos 2x) dx=(1)/(sqrt(2)) sin (2x-k)+c " then " k=?`

Last Answer : `" if " int (sin 2x- cos 2x) dx=(1)/(sqrt(2)) sin (2x-k)+c " then " k=?` A. `-(5pi)/(4)` B. `(pi)/(4)` C. `-(pi)/(4)` D.

`int_(0)^(pi//2) x sin cos x dx=?`

Description : `int_(0)^(pi//2) x sin cos x dx=?`

Last Answer : `int_(0)^(pi//2) x sin cos x dx=?` A. `(pi)/(4)` B. `(pi)/(8)` C. `(pi)/(12)` D.

`int sin^(3) x cos^(3) x dx =?`

Description : `int sin^(3) x cos^(3) x dx =?`

Last Answer : `int sin^(3) x cos^(3) x dx =?` A. `(1)/(4) sin^(4) x + (1)/(6) sin^(6) x+c` B. `(1)/(4) cos^(4)x-(1)/(6) cos^(6) x+c` C. none of the above D.

`int(sin x)/( sqrt(1+cos x))dx=?`

Description : `int(sin x)/( sqrt(1+cos x))dx=?`

Last Answer : `int(sin x)/( sqrt(1+cos x))dx=?` A. `sqrt(1+cos x) +c` B. `-2sqrt(1+ cos x)+c` C. `2sqrt(1+ cos x) +c` D.

`int (1)/(sin^(2) x cos^(2)x) dx=?`

Description : `int (1)/(sin^(2) x cos^(2)x) dx=?`

Last Answer : `int (1)/(sin^(2) x cos^(2)x) dx=?` A. `tan x-cot x+c` B. `sec x+ cosec x+c` C. `sec x- cosec x+c` D.

`int_(0)^(pi) x sin x. cos^(2) x dx`

Description : `int_(0)^(pi) x sin x. cos^(2) x dx`

Last Answer : `int_(0)^(pi) x sin x. cos^(2) x dx`

`int_(0)^(pi//2) x sin x cos x dx`

Description : `int_(0)^(pi//2) x sin x cos x dx`

Last Answer : `int_(0)^(pi//2) x sin x cos x dx`

` int (3-4 sin x)/(cos^(2) x) dx=?`

Description : ` int (3-4 sin x)/(cos^(2) x) dx=?`

Last Answer : ` int (3-4 sin x)/(cos^(2) x) dx=?` A. `4 tan x +4 sec x+c` B. ` 3 tan x + 4 sec x+ c` C. ` 4 tan x +3 sec x+c` D.

`int_(0)^(pi//2) e^(x) (sin x + cos x) dx`

Description : `int_(0)^(pi//2) e^(x) (sin x + cos x) dx`

Last Answer : `int_(0)^(pi//2) e^(x) (sin x + cos x) dx`

`(i) int_(0)^(pi//4) e^(tanx) . sec^(2) x dx` `(ii) int_(0)^(pi//4) (sin (cos 2x))/(" cosec " 2x)dx`

Description : `(i) int_(0)^(pi//4) e^(tanx) . sec^(2) x dx` `(ii) int_(0)^(pi//4) (sin (cos 2x))/(" cosec " 2x)dx`

Last Answer : `(i) int_(0)^(pi//4) e^(tanx) . sec^(2) x dx` `(ii) int_(0)^(pi//4) (sin (cos 2x))/(" cosec " 2x)dx`

`int_(0)^(pi//2) sin^(2) x cos ^(2) x dx`

Description : `int_(0)^(pi//2) sin^(2) x cos ^(2) x dx`

Last Answer : `int_(0)^(pi//2) sin^(2) x cos ^(2) x dx`

`int_(0)^(pi//2) (a cos^(2) x+b sin^(2) x) dx`

Description : `int_(0)^(pi//2) (a cos^(2) x+b sin^(2) x) dx`

Last Answer : `int_(0)^(pi//2) (a cos^(2) x+b sin^(2) x) dx`

`(i) int_(0)^(pi//2) x sin x cos x dx` `(ii) int_(0)^(pi//6) (2+3x^(2)) cos 3x dx`

Description : `(i) int_(0)^(pi//2) x sin x cos x dx` `(ii) int_(0)^(pi//6) (2+3x^(2)) cos 3x dx`

Last Answer : `(i) int_(0)^(pi//2) x sin x cos x dx` `(ii) int_(0)^(pi//6) (2+3x^(2)) cos 3x dx`

`int(1)/(3+2 sin x +cos x)dx`

Description : `int(1)/(3+2 sin x +cos x)dx`

Last Answer : `int(1)/(3+2 sin x +cos x)dx`

`int(1)/((sin x-2 cos x) (2 sin x+c osx))dx`

Description : `int(1)/((sin x-2 cos x) (2 sin x+c osx))dx`

Last Answer : `int(1)/((sin x-2 cos x) (2 sin x+c osx))dx`

`int(1)/(sin x cos x + 2cos^(2)x)dx`

Description : `int(1)/(sin x cos x + 2cos^(2)x)dx`

Last Answer : `int(1)/(sin x cos x + 2cos^(2)x)dx`

`int(1)/(cos^(2) x-3 sin^(2) x)dx`

Description : `int(1)/(cos^(2) x-3 sin^(2) x)dx`

Last Answer : `int(1)/(cos^(2) x-3 sin^(2) x)dx`

`int(1)/(sin^(2)x-4 cos^(2)x)dx`

Description : `int(1)/(sin^(2)x-4 cos^(2)x)dx`

Last Answer : `int(1)/(sin^(2)x-4 cos^(2)x)dx`