rsin−1x=a,rcos−1x=b,rtan−1y=cSo, a+b=2rπ
cos(a+bπc)=cos(2rπrπtan−1y)
=cos(2tan−1y), let tan−1y=θ
=cos(2θ)
=1+tan2θ1−tan2θ=1+y21−y2
JEE Main 2021 — Mathematics Trigonometry
If asin−1x=bcos−1x=ctan−1y;0<x<1, then the value of cos(a+bπc) is:
Held on 26 Feb 2021 · Verified 6 Jul 2026.
1+y21−y2
1−y2
yy1−y2
2y1−y2
Sign in to track your attempts and accuracy.
Sign in to keep a private note on this question. Nothing you write is ever public.
If $\sin\left(\dfrac{\pi}{18}\right) \sin\left(\dfrac{5\pi}{18}\right) \sin\left(\dfrac{7\pi}{18}\right) = K$, then the value of $\sin\left(\dfrac{10K\pi}{3}\right)$ is :
If $\frac{\cos ^{2} 48^{\circ}-\sin ^{2} 12^{\circ}}{\sin ^{2} 24^{\circ}-\sin ^{2} 6^{\circ}}=\frac{\alpha+\beta \sqrt{5}}{2}$, where $\alpha, \beta \in \mathbb{N}$, then $\alpha+\beta$ is equal to $\_\_\_\_\_$
The value of sin²30° + cos²30° is:
Considering the principal values of inverse trigonometric functions, the value of the expression $\tan \left(2 \sin ^{-1}\left(\frac{2}{\sqrt{13}}\right)-2 \cos ^{-1}\left(\frac{3}{\sqrt{10}}\right)\right)$ is equal to :
Let $\alpha$ and $\beta$ respectively be the maximum and the minimum values of the function $f(\theta)=4\left(\sin ^{4}\left(\frac{7 \pi}{2}-\theta\right)+\sin ^{4}(11 \pi+\theta)\right)-2\left(\sin ^{6}\left(\frac{3 \pi}{2}-\theta\right)+\sin ^{6}(9 \pi-\theta)\right), \theta \in \mathbf{R}$. Then $\alpha+2 \beta$ is equal to :
Work through every JEE Main Trigonometry PYQ, year by year.