31
MCQ (Single Correct Answer)
If $\sin ^{-1}\left(\frac{2 a}{1+a^2}\right)+\cos ^{-1}\left(\frac{1-a^2}{1+a^2}\right)=\tan ^{-1}\left(\frac{2 x}{1-x^2}\right)$, where $\left.a, x \in\right] 0,1[$, then the value of $x$ is
A
0
B
$\frac{a}{2}$
C
a
D
$\frac{2 a}{1-a^2}$
32
MCQ (Single Correct Answer)
The value of $\cot \left[\cos ^{-1}\left(\frac{7}{25}\right)\right]$ is
A
$\frac{25}{24}$
B
$\frac{25}{7}$
C
$\frac{24}{25}$
D
$\frac{7}{24}$
33
MCQ (Single Correct Answer)
The value of $\tan \left(\frac{1}{2} \cos ^{-1} \frac{2}{\sqrt{5}}\right)$ is
A
$2+\sqrt{5}$
B
$\sqrt{5}-2$
C
$\frac{\sqrt{5}+2}{2}$
D
$5+\sqrt{2}$
34
MCQ (Single Correct Answer)
If $|x| \leq 1$, then $2 \tan ^{-1} x+\sin ^{-1}\left(\frac{2 x}{1+x^2}\right)$ is equal to
A
$4 \tan ^{-1} x$
B
0
C
$\frac{\pi}{2}$
D
$\pi$
35
MCQ (Single Correct Answer)
If $\cos ^{-1} \alpha+\cos ^{-1} \beta+\cos ^{-1} \gamma=3 \pi$, then $\alpha(\beta+\gamma)+\beta(\gamma+\alpha)+\gamma(\alpha+\beta)$ equals to
A
0
B
1
C
6
D
12