1
VITEEE 2022
MCQ (Single Correct Answer)
+1
-0

If $$\cos ^{-1} x-\cos ^{-1} \frac{y}{2}=\alpha$$ where $$-1 \leq x \leq 1, -2 \leq y \leq 2, x \leq \frac{y}{2}$$, then for all $$x, y, 4 x^2-4 x y \cos \alpha+y^2$$ is equal to

A
$$2 \sin ^2 \alpha$$
B
$$4 \cos ^2 \alpha+2 x^2 y^2$$
C
$$4 \sin ^2 \alpha$$
D
$$4 \sin ^2 \alpha-2 x^2 y^2$$
2
VITEEE 2021
MCQ (Single Correct Answer)
+1
-0

Using the principal values, the value of $$\sin ^{-1}\left\{\sin \frac{5 \pi}{6}\right\}+\tan ^{-1}\left\{\tan \frac{\pi}{6}\right\}$$ is equal to

A
$$\frac{\pi}{6}$$
B
$$\frac{2 \pi}{3}$$
C
$$\frac{\pi}{3}$$
D
$$\frac{5 \pi}{6}$$
3
VITEEE 2021
MCQ (Single Correct Answer)
+1
-0

Find the value of $$\cos ^{-1}\left(\frac{4}{5}\right)+\tan ^{-1}\left(\frac{3}{5}\right)$$.

A
$$\tan ^{-1}\left(\frac{7}{10}\right)$$
B
$$\tan ^{-1}\left(\frac{27}{11}\right)$$
C
$$\sin ^{-1}\left(\frac{7}{5}\right)$$
D
$$\tan ^{-1}\left(\frac{1}{5}\right)$$
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