Statement-1: `cosec^(-1)(3)/(2)+cos^(-1)(2/3)-2cot^(-1)(1/7)-cot^(-1)7=cot^(-1)7` Statement-2: `cos^(-1)x=sin^(-1)((1)/(x)) and for xgt0cot^(-1)x=tan^(-1)((1)/(x))`

Options

A. Statement-1 is is True, Statement-2 is true, Statement-2 is a correct explanation for Statement-1.
B. Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.
C. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False, Statement-2 is True.

Explanation

To solve the given problem, we need to analyze both statements and determine their validity step by step.

### Statement 1:
We need to verify if the following equation holds true:
\[ \frac{\csc^{-1}(3)}{2} + \cos^{-1}\left(\frac{2}{3}\right) - 2\cot^{-1}\left(\frac{1}{7}\right) - \cot^{-1}(7) = \cot^{-1}(7) \]

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