1
JEE Main 2022 (Online) 28th July Evening Shift
+4
-1

The sum of the absolute maximum and absolute minimum values of the function $$f(x)=\tan ^{-1}(\sin x-\cos x)$$ in the interval $$[0, \pi]$$ is :

A
0
B
$$\tan ^{-1}\left(\frac{1}{\sqrt{2}}\right)-\frac{\pi}{4}$$
C
$$\cos ^{-1}\left(\frac{1}{\sqrt{3}}\right)-\frac{\pi}{4}$$
D
$$\frac{-\pi}{12}$$
2
JEE Main 2022 (Online) 28th July Morning Shift
+4
-1

Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the equation $$\cos ^{-1}(x)-2 \sin ^{-1}(x)=\cos ^{-1}(2 x)$$ is equal to :

A
0
B
1
C
$$\frac{1}{2}$$
D
$$-\frac{1}{2}$$
3
JEE Main 2022 (Online) 26th July Evening Shift
+4
-1

If $$0 < x < {1 \over {\sqrt 2 }}$$ and $${{{{\sin }^{ - 1}}x} \over \alpha } = {{{{\cos }^{ - 1}}x} \over \beta }$$, then the value of $$\sin \left( {{{2\pi \alpha } \over {\alpha + \beta }}} \right)$$ is

A
$$4 \sqrt{\left(1-x^{2}\right)}\left(1-2 x^{2}\right)$$
B
$$4 x \sqrt{\left(1-x^{2}\right)}\left(1-2 x^{2}\right)$$
C
$$2 x \sqrt{\left(1-x^{2}\right)}\left(1-4 x^{2}\right)$$
D
$$4 \sqrt{\left(1-x^{2}\right)}\left(1-4 x^{2}\right)$$
4
JEE Main 2022 (Online) 26th July Morning Shift
+4
-1

$$\tan \left(2 \tan ^{-1} \frac{1}{5}+\sec ^{-1} \frac{\sqrt{5}}{2}+2 \tan ^{-1} \frac{1}{8}\right)$$ is equal to :

A
1
B
2
C
$$\frac{1}{4}$$
D
$$\frac{5}{4}$$
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