Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Advanced
Exam
JEE Advanced
Subject
Mathematics
Chapter
Trigonometry

JEE Advanced · Mathematics · Trigonometry

If (θ-α), 3 θ, (θ+α) are in A.P. and θ is not an integral multiple...

If cot⁡(θ−α),3cot⁡θ,cot⁡(θ+α)\cot (\theta-\alpha), 3 \cot \theta, \cot (\theta+\alpha) are in A.P. and θ\theta is not an integral multiple of π2\frac{\pi}{2}, then find the value of 2sin⁡2θsin⁡2α\frac{2 \sin ^2 \theta}{\sin ^2 \alpha}.

Correct answer

3

Step-by-step solution

6cot⁡θ=cot⁡(θ−α)+cot⁡(θ+α)66cot⁡θ=cos⁡(θ−α)sin⁡(θ−α)+cos⁡(θ+α)sin⁡(θ+α)6cot⁡θ=sin⁡2θsin⁡2θ−sin⁡2α=2sin⁡θcos⁡θsin⁡2θ−sin⁡2α3sin⁡θ=sin⁡θsin⁡2θ−sin⁡2α3sin⁡2θ−3sin⁡2α=sin⁡2θ⇒2sin⁡2θsin⁡2α=3\begin{aligned} 6 \cot \theta & =\cot (\theta-\alpha)+\cot (\theta+\alpha) \\ 6 \quad 6 \cot \theta & =\frac{\cos (\theta-\alpha)}{\sin (\theta-\alpha)}+\frac{\cos (\theta+\alpha)}{\sin (\theta+\alpha)} \\ 6 \cot \theta & =\frac{\sin 2 \theta}{\sin ^2 \theta-\sin ^2 \alpha}=\frac{2 \sin \theta \cos \theta}{\sin ^2 \theta-\sin ^2 \alpha} \\ \frac{3}{\sin \theta} & =\frac{\sin \theta}{\sin ^2 \theta-\sin ^2 \alpha} \\ 3 \sin ^2 \theta-3 \sin ^2 \alpha & =\sin ^2 \theta \Rightarrow \frac{2 \sin ^2 \theta}{\sin ^2 \alpha}=3\end{aligned}
Practice Trigonometry on Quantrex Academy →

More from Trigonometry

The number of real root(s) of the equation x^2 x=1 lie(s) between 0 and 2 π is/are Most Important Selected Qs for JEE AdvancedIf |x^2-(π)/(4)+ x-2|=|x^2-2|+| x|+(π)/(4) then Most Important Selected Qs for JEE AdvancedIf 3 x+ (2 x-(7 π)/(6))=-2 , then x is equal to ( where m ∈ I) Most Important Selected Qs for JEE AdvancedWhat is the minimum value of ( ^4 α)/( ^2 β)+( ^4 β)/( ^2 α) for α, B ≠ (k π)/(2), k ∈ Z ? Most Important Selected Qs for JEE AdvancedIf x+ y ≥ α x x ∈ R then y+ α is equal to Most Important Selected Qs for JEE AdvancedIf A, B are the roots of the quadratic equation a b x^2-c^2 x+a b=0 where a, b, c are… Most Important Selected Qs for JEE AdvancedIf θ and - θ are the roots of the equation a x^2-b x-c=0 , where a, b, c are the sides of… Most Important Selected Qs for JEE AdvancedIf 2 ^2((π)/(2) ^2 x)=1- (π 2 x), x ≠(2 n+1) (π)/(2), n ∈ I , then Most Important Selected Qs for JEE AdvancedConsider the equation 1+ 3 2 x ^4 x+4 ^2 x + ^4 x+4 ^2 x = 2 ^ -1 ( 2 x) x ∈(-π, π) Most Important Selected Qs for JEE AdvancedSet of values of x of the equation 2 x= ( ^3 x- ^3 x) is - Most Important Selected Qs for JEE AdvancedIf 4+ 8- 32+ 768 =a 2 \ left((11 π)/(b)), where a and b are natural numbers then (b)/(a)… Most Important Selected Qs for JEE AdvancedIf a x+ x+1=cosec x then the possible values of x can be Most Important Selected Qs for JEE AdvancedFor the equation 2( x- 2 x)- 2 x(1+2 x)+2 x=0, x ∈[0,2 π]- Most Important Selected Qs for JEE AdvancedWhich of the following set of values of x satisfies the equation 2^ (2 ^2 x-3 x+1) +2^… Most Important Selected Qs for JEE AdvancedIf α satisfies the equation 2 2 ^3 x-54 2 ^3 x=19 , then possible value of ( .2 ^2 α+ 2… Most Important Selected Qs for JEE AdvancedIf f(x)=(3)/(1+ ^2 x)+(9)/(1+ ^2 x) , then : Most Important Selected Qs for JEE Advanced Full Trigonometry list Trigonometry JEE Maths PYQsJEE Mathematics PYQs All Most Important Selected Qs for JEE Advanced PYQs