JEE Main 2026 (Online) 8th April Evening ShiftQuestion 1
Let $\alpha=3\sin^{-1}\left(\frac{6}{11}\right)$ and $\beta=3\cos^{-1}\left(\frac{4}{9}\right)$, where inverse trigonometric functions take only the principal values.
Given below are two statements :
Statement I : $\cos(\alpha+\beta)>0$.
Statement II : $\cos(\alpha)<0$.
In the light of the above statements, choose the correct answer from the options given below :
Inverse Trigonometric Functions
Solution
$\sin^{-1}(6/11)\approx0.5760$ rad, so $\alpha\approx1.728$ rad $>\pi/2$, hence $\cos\alpha<0$ (numerically $-0.159$): Statement II true. $\cos^{-1}(4/9)\approx1.1141$ rad, $\beta\approx3.342$ rad. $\alpha+\beta\approx5.070$ rad, in $(3\pi/2,2\pi)$, so $\cos(\alpha+\beta)\approx0.342>0$: Statement I true. Both true: option (A).