Match List-I with List-II regarding the value of the following.

Choose the correct answer from the options given below:

(A)-(III), (B)-(IV), (C)-(I), (D)-(II)

The correct answer is Option (3) → (A)-(III), (B)-(IV), (C)-(I), (D)-(II)

(A) $\cos^{-1}(\cos\frac{7\pi }{6})=\cos^{-1}(-\frac{\sqrt{3}}{2})$

$=\pi - \frac{\pi}{6}=\frac{5\pi }{6}$ (III)

(B) $\cos^{-1}(\cos\frac{5\pi }{4})=\cos^{-1}(-\frac{1}{\sqrt{2}})$

$=\pi - \frac{\pi}{4}=\frac{3\pi }{4}$ (IV)

(C) $\sin^{-1}\frac{4}{5}+2\tan^{-1}\frac{1}{3}$

$=\tan^{-1}\frac{4}{3}+\tan^{-1}\frac{2×\frac{1}{3}}{1-\frac{1}{9}}$

$=\tan^{-1}\frac{4}{3}+\tan^{-1}\frac{3}{4}=\frac{\pi}{2}$ (I)

(D) $\tan^{-1}\frac{x}{y}-\tan^{-1}\frac{x-y}{x+y}$

$=\tan^{-1}\frac{x}{y}-\tan^{-1}\frac{\frac{x}{y}-1}{\frac{x}{y}+1}=\tan^{-1}\frac{x}{y}-\tan^{-1}\frac{x}{y}+\tan^{-1}1=\frac{\pi}{4}$ (II)