The value of $\cos^{-1}\left\{\dfrac{\sin x+\cos x}{\sqrt{2}}\right\}, \dfrac{5\pi}{4} < x < \dfrac{9\pi}{4}$ is :

$\cos^{-1}\left(\cos\frac{7\pi}{6}\right)$ equals:

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

The value of $\cos(2\cos^{-1}x + \sin^{-1}x)$ at $x = \frac{1}{5}$ is

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:

The graph of $\sin^{-1} x$ is represented by:

$\sin^{-1}(\cos\frac{3\pi}{5})$ equals