Description : If `sin theta+ sin^2theta+ sin^3theta=1` ,prove that `cos^6theta-4 cos^4theta+8cos^2= 4`
Last Answer : If `sin theta+ sin^2theta+ sin^3theta=1` ,prove that `cos^6theta-4 cos^4theta+8cos^2= 4`
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.
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
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
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`
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.
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)`
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)}`
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
Description : The positive integer value of `n gt 3` satisfying the equation `(1)/(sin((pi)/(n)))=(1)/(sin((2pi)/(n)))+(1)/(sin((3pi)/(n)))` is
Last Answer : The positive integer value of `n gt 3` satisfying the equation `(1)/(sin((pi)/(n)))=(1)/(sin((2pi)/(n)))+(1)/(sin((3pi)/(n)))` is
Description : The number of values of `theta` in the interval `(-pi/2,pi/2)` such that `theta != npi/5` for `ninN` and `tan theta = cot 5theta` as well as `sin2thet
Last Answer : The number of values of `theta` in the interval `(-pi/2,pi/2)` such that `theta != npi/5` for ... = cot 5theta` as well as `sin2theta = cos 4theta` is
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.
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.
Description : `int_(0)^(pi) x sin x. cos^(2) x dx`
Last Answer : `int_(0)^(pi) x sin x. cos^(2) 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`
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`
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`
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`
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`
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`
Description : No. of solutions of `16^(sin^2x)+16^(cos^2x)=10, 0 le x le 2 pi` is
Last Answer : No. of solutions of `16^(sin^2x)+16^(cos^2x)=10, 0 le x le 2 pi` is
Description : If `sin^4 alpha + 4 cos^4 beta + 2 = 4sqrt2 sin alpha cos beta ; alpha, beta in [0,pi],` then `cos(alpha+beta) - cos(alpha - beta)` is equal to :
Last Answer : If `sin^4 alpha + 4 cos^4 beta + 2 = 4sqrt2 sin alpha cos beta ; alpha, beta in [0,pi],` then `cos(alpha+beta ... sqrt(2)` B. `0` C. `sqrt(2)` D. `-1`
Description : Let `cos(alpha+beta)=(4)/(5)` and let `sin(alpha-beta)=(5)/(13)`, where `0 le alpha`, `beta=(pi)/(4)`. Then`tan2alpha=`
Last Answer : Let `cos(alpha+beta)=(4)/(5)` and let `sin(alpha-beta)=(5)/(13)`, where `0 le alpha`, `beta=(pi)/(4)`. Then ... 19)/(12)` C. `(20)/(7)` D. `(25)/(16)`
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
Description : If the sum of all the solutions of the equation `8 cosx.(cos(pi/6+x)cos(pi/6-x)-1/2)=1` in `[0,pi]` is `k pi` then k is equal to
Last Answer : If the sum of all the solutions of the equation `8 cosx.(cos(pi/6+x)cos(pi/6-x)-1/2)=1` in `[0,pi]` is `k pi` ... (20)/(9)` C. `(2)/(3)` D. `(13)/(9)`
Description : If `alpha, beta` are the roots of the equation `x^2 + (sin phi -1)x-1/2 cos^2 phi = 0 (phi in R),` then the maximum value of the sum of the squares of
Last Answer : If `alpha, beta` are the roots of the equation `x^2 + (sin phi -1)x-1/2 cos^2 phi = 0 (phi in R),` then ... the roots is. A. 4 B. 3 C. `9//4` D. 2
Description : Find the maximum and minimum values of the function `f(x) = x+ sin 2x, (0 lt x lt pi)`.
Last Answer : Find the maximum and minimum values of the function `f(x) = x+ sin 2x, (0 lt x lt pi)`.
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.
Description : Let `-1/6 < theta < -pi/12` Suppose `alpha_1 and beta_1`, are the roots of the equation `x^2-2xsectheta + 1=0` and `alpha_2 and beta_2` are the
Last Answer : Let `-1/6 < theta < -pi/12` Suppose `alpha_1 and beta_1`, are the roots of the equation `x^2-2xsectheta ... )` B. `2sectheta` C. `-2tantheta` D. `0`
Description : Solve the following equation `(i) 5cos2theta+2cos^(2)"(theta)/(2)+1=0`, `-(pi)/(2) lt theta lt (pi)/(2)` `(ii) sin7theta+sin4theta+sintheta=0`, `0 le
Last Answer : Solve the following equation `(i) 5cos2theta+2cos^(2)"(theta)/(2)+1=0`, `-(pi)/(2) lt theta ... iii) tantheta+sectheta=sqrt(3)`, `0 le theta le 2pi`
Description : Find the maximum and minimum values of the function `f(x) = sin x + cos 2x`.
Last Answer : Find the maximum and minimum values of the function `f(x) = sin x + cos 2x`.
Description : for `0ltthetaltpi/2 ` the solution(s) of ` sum_(m=1)^6c o s e c(theta+((m-1)pi)/4)c o s e c(theta+(mpi)/n)=4sqrt(2)` is (are):
Last Answer : for `0ltthetaltpi/2 ` the solution(s) of ` sum_(m=1)^6c o s e c(theta+((m-1)pi)/4)c o s e c(theta+(mpi)/n ... (pi)/(6)` C. `(pi)/(12)` D. `(5pi)/(12)`
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
Description : If sin theta equals 3/4 and theta is in quadrant II what is the value of tan theta?
Last Answer : 0.75
Description : `int_(0)^(pi//2) (dx)/(1+2 cos x)`
Last Answer : `int_(0)^(pi//2) (dx)/(1+2 cos x)`
Description : `int_(0)^(pi) (1)/(5+2 cos x)dx`
Last Answer : `int_(0)^(pi) (1)/(5+2 cos x)dx`
Description : `int_(0)^(pi//2) (1)/(4+3 cos x)dx`
Last Answer : `int_(0)^(pi//2) (1)/(4+3 cos x)dx`
Description : `int_(0)^(pi//2) (dx)/(4sin^(2) x + 5 cos^(2)x)`
Last Answer : `int_(0)^(pi//2) (dx)/(4sin^(2) x + 5 cos^(2)x)`
Description : `int_(0)^(pi//4) cos 0. " cosec"^(2) 0 do`
Last Answer : `int_(0)^(pi//4) cos 0. " cosec"^(2) 0 do`
Description : `int_(0)^(pi//4) (1)/(1+cos 2x)dx`
Last Answer : `int_(0)^(pi//4) (1)/(1+cos 2x)dx`
Description : ` int_(0)^(pi//6) cos x cos 3x dx`
Last Answer : ` int_(0)^(pi//6) cos x cos 3x dx`
Description : `(i) int_(0)^(pi//2) x cos x dx` (i) `int_(1)^(3) x. log x dx`
Last Answer : `(i) int_(0)^(pi//2) x cos x dx` (i) `int_(1)^(3) x. log x dx`
Description : `int_(0)^(pi//2) x^(2) cos x dx`
Last Answer : `int_(0)^(pi//2) x^(2) cos x dx`
Description : `int_(0)^(pi//2) sqrt(1- cos 2x) dx`
Last Answer : `int_(0)^(pi//2) sqrt(1- cos 2x) dx`
Description : `int_(0)^(pi//2) cos 3x dx`
Last Answer : `int_(0)^(pi//2) cos 3x dx`
Description : If the arithmetic mean of the roots of the equation `4cos^(3)x-4cos^(2)x-cos(pi+x)-1=0` in the interval `[0,315]` is equal to `kpi`, then the value of
Last Answer : If the arithmetic mean of the roots of the equation `4cos^(3)x-4cos^(2)x-cos(pi+x)-1=0` in the interval `[0,315 ... is A. `10` B. `20` C. `50` D. `80`
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:
Description : Find the intervals in which the function `f(x) = sin x +cos x,x in [0, 2pi]` is (i) strictly increasing, (ii) strictly decreasing.
Last Answer : Find the intervals in which the function `f(x) = sin x +cos x,x in [0, 2pi]` is (i) strictly increasing, (ii) strictly decreasing.
Description : The number of distinct solutions of the equation `5/4cos^(2)2x + cos^4 x + sin^4 x+cos^6x+sin^6 x =2` in the interval `[0,2pi] ` is
Last Answer : The number of distinct solutions of the equation `5/4cos^(2)2x + cos^4 x + sin^4 x+cos^6x+sin^6 x =2` in the interval `[0,2pi] ` is