Arrange the principal values of the following functions in ascending order

(A) $\cosec^{-1}(2)$

(B) $\tan^{-1}(-\sqrt{3})$

(C) $\tan^{-1}(1)$

(D) $\tan^{-1}\left(\cos\frac{3\pi}{7}\right)$

Choose the correct answer from the options given below:

Match List-I with List-II

Choose the correct answer from the options given below:

$\cos[\tan^{-1}\{\sin(\cot^{-1}x)\}]$ is equal to

The principal value of $\cot^{-1}\left(-\frac{1}{\sqrt{3}}\right)$

For the principal value branch, the value of $\sin\left(\frac{\pi}{2} - \sin^{-1}\left(-\frac{\sqrt{3}}{2}\right)\right)$ is

$\tan(\alpha + \beta) =$

Consider $f(x) = \sin(3x) + 4, \forall x \in \mathbb{R}$. Then

(A) Maximum value of $f(x)$ is 5

(B) Minimum value of $f(x)$ is 3

(C) Maximum value of $f(x)$ is attained at $x = \frac{\pi}{6}$

(D) Minimum value of $f(x)$ is attained at $x = 0$

Choose the correct answer from the options given below: