`tan^(-1)sqrt(3)-sec^(-1)(-2)`is equal to(a) `pi` (B) `-pi/3`(C) `pi/3` (D) `(2pi)/3`

Options

A. `pi`
B. `-(pi)/(3)`
C. `(pi)/(3)`
D. `(2pi)/(3)`

Explanation

To solve the expression \( \tan^{-1}(\sqrt{3}) - \sec^{-1}(-2) \), we will evaluate each term separately and then combine the results.

### Step-by-Step Solution

1. **Evaluate \( \tan^{-1}(\sqrt{3}) \)**:
- Let \( y = \tan^{-1}(\sqrt{3}) \).
- This implies \( \tan(y) = \sqrt{3} \).
- We know that \( \tan\left(\frac{\pi}{3}\right) = \sqrt{3} \).
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