1
MHT CET 2021 23th September Morning Shift
+2
-0

If $$\tan ^{-1}\left[\frac{\sqrt{1+x^2}-\sqrt{1-x^2}}{\sqrt{1+x^2}+\sqrt{1-x^2}}\right]=\alpha$$, then the value of $$\sin 2 \alpha$$ is

A
$$x^3$$
B
$$\sqrt{x}$$
C
$$x$$
D
$$\mathrm{x}^2$$
2
MHT CET 2021 22th September Evening Shift
+2
-0

If $$2 \tan ^{-1}(\cos x)=\tan ^{-1}(2 \operatorname{cosec} x)$$, then the value of $$x$$ is

A
$$\frac{\pi^{\mathrm{c}}}{6}$$
B
$$\frac{\pi^{\mathrm{c}}}{4}$$
C
$$\frac{\pi^{\mathrm{c}}}{3}$$
D
$$\frac{\pi^{\mathrm{c}}}{12}$$
3
MHT CET 2021 22th September Morning Shift
+2
-0

$$\tan ^{-1}\left(\tan \frac{5 \pi}{6}\right)+\cos ^{-1}\left(\cos \frac{13 \pi}{6}\right)=$$

A
0
B
$$3 \pi$$
C
$$\frac{-\pi}{6}$$
D
$$\frac{\pi}{6}$$
4
MHT CET 2021 22th September Morning Shift
+2
-0

$$y=\tan ^{-1}\left(\sqrt{\frac{1+\sin x}{1-\sin x}}\right), 0 \leq x < \frac{\pi}{2}$$, then $$\frac{d y}{d x}$$ at $$x=\frac{\pi}{6}$$ is

A
$$\frac{1}{4}$$
B
$$\frac{-1}{4}$$
C
$$\frac{-3}{2}$$
D
$$\frac{1}{2}$$
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