The value of
`cot^(-1)(-1)+cosec^(-1)(-sqrt(2))+sec^(-1)(2)` is

Options

A. `(5pi)/(6)`
B. `(2pi)/(3)`
C. `(7pi)/(6)`
D. `(pi)/(6)`

Explanation

To solve the expression \( \cot^{-1}(-1) + \csc^{-1}(-\sqrt{2}) + \sec^{-1}(2) \), we will evaluate each term step by step.

### Step 1: Evaluate \( \cot^{-1}(-1) \)

The cotangent function is negative in the second and fourth quadrants. The value of \( \cot^{-1}(-1) \) corresponds to an angle where the cotangent is -1. The angle that satisfies this condition in the range \( (0, \pi) \) (the range of \( \cot^{-1} \)) is:

\[
\cot^{-1}(-1) = \frac{3\pi}{4}
...