MHT-CET

Inverse Trigonometric Fun question bank (Mathematics)

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Q1.

The value of $\tan \left\{\frac{1}{2} \sin ^{-1}\left(\frac{2 x}{1+x^2}\right)+\frac{1}{2} \cos ^{-1}\left(\frac{1-y^2}{1+y^2}\right)\right\}$ is

(A)

$\frac{x+y}{1-x y}$

(B)

$\frac{x-y}{1+x y}$

(C)

$\frac{x-y}{1-x y}$

(D)

$\frac{x+y}{1+x y}$

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Q2.

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 $x, y 4 x^2-4 x y \cos a+y^2$ is equal to

(A)

$2 \sin ^2 a$

(B)

$4 \sin ^2 a$

(C)

$4 \cos ^2 a+2 x^2 y^2$

(D)

$4 \sin ^2 a-2 x^2 y^2$

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