# Let A = cos sin sin cos é ù a- a ê ú ë û a a , (aÎ R) such that A32 = 0 1 1 0 é ù – ê ú ë û . Then a value of a is :

Question:

Let $\mathrm{A}=\left[\begin{array}{cr}\cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha\end{array}\right],(\alpha \in \mathrm{R})$ such that $\mathrm{A}^{32}=\left[\begin{array}{cc}0 & -1 \\ 1 & 0\end{array}\right]$. Then a value of $\alpha$ is :

1. $\frac{\pi}{32}$

2. 0

3. $\frac{\pi}{64}$

4. $\frac{\pi}{16}$

Correct Option: 3

JEE Main Previous Year 1 Question of JEE Main from Mathematics Inverse Trigonometric Functions chapter.
JEE Main Previous Year April 8, 2019 (I)

Solution:

### Related Questions

• If $\alpha=\cos ^{-1}\left(\frac{3}{5}\right), \beta=\tan ^{-1}\left(\frac{1}{3}\right)$, where $0<\alpha, \beta<\frac{\pi}{2}$, then $\alpha-\beta$ is equal to:

View Solution

• A value of $x$ satisfying the equation $\sin \left[\cot ^{-1}(1+x)\right]=\cos$ $\left[\tan ^{-1} x\right]$, is :

View Solution

• The principal value of $\tan ^{-1}\left(\cot \frac{43 \pi}{4}\right)$ is:

View Solution

• The number of solutions of the equation, $\sin ^{-1} x=2 \tan ^{-1} x$ (in principal values) is :

View Solution

• A value of $\tan ^{-1}\left(\sin \left(\cos ^{-1}\left(\sqrt{\frac{2}{3}}\right)\right)\right.$ is

View Solution

• A value of $\tan ^{-1}\left(\sin \left(\cos ^{-1}\left(\sqrt{\frac{2}{3}}\right)\right)\right.$ is

View Solution

• The largest interval lying in $\left(\frac{-\pi}{2}, \frac{\pi}{2}\right)$ for which the function, $f(x)=4^{-x^{2}}+\cos ^{-1}\left(\frac{x}{2}-1\right)+\log (\cos x)$, is defined, is

View Solution

• The domain of the function $f(x)=\frac{\sin ^{-1}(x-3)}{\sqrt{9-x^{2}}}$ is

View Solution

• The trigonometric equation $\sin ^{-1} x=2 \sin ^{-1} a$ has a solution for

View Solution

• $$\cot ^{-1}(\sqrt{\cos \alpha})-\tan ^{-1}(\sqrt{\cos \alpha})=x$$ then $\sin x=$

View Solution

error: Content is protected !!