1
BITSAT 2023
MCQ (Single Correct Answer)
+3
-1

If $$\cot ^{-1} \sqrt{\cos \alpha}-\tan ^{-1} \sqrt{\cos \alpha}=x$$, then $$\sin x$$ is equal to

A
$$\cot ^2\left(\frac{\alpha}{2}\right)$$
B
$$\tan ^2\left(\frac{\alpha}{2}\right)$$
C
$$\cot \left(\frac{\alpha}{2}\right)$$
D
$$\tan \alpha$$
2
BITSAT 2022
MCQ (Single Correct Answer)
+3
-1

If $$x \in \left( {0,{\pi \over 2}} \right)$$, then the value of $${\cos ^{ - 1}}\left( {{7 \over 2}(1 + \cos 2x) + \sqrt {({{\sin }^2}x - 48{{\cos }^2}x)\sin x} } \right)$$ is equal to

A
$$x - {\cos ^{ - 1}}(7\cos x)$$
B
$$x + {\sin ^{ - 1}}(7\cos x)$$
C
$$x + {\cos ^{ - 1}}(6\cos x)$$
D
$$x + {\cos ^{ - 1}}(7\cos x)$$
3
BITSAT 2021
MCQ (Single Correct Answer)
+3
-1

The minimum value of $${({\sin ^{ - 1}}x)^3} + {({\cos ^{ - 1}}x)^3}$$ is equal to

A
$${{{\pi ^3}} \over {32}}$$
B
$${{5{\pi ^3}} \over {32}}$$
C
$${{9{\pi ^3}} \over {32}}$$
D
$${{11{\pi ^3}} \over {32}}$$
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