The value of `cot((7pi)/16)+2cot((3pi)/8)+cot((15pi)/16)` is (a)`4` (b)` 2` (c) `-2` (d) `-4`

Explanation

To solve the expression \( \cot\left(\frac{7\pi}{16}\right) + 2\cot\left(\frac{3\pi}{8}\right) + \cot\left(\frac{15\pi}{16}\right) \), we can follow these steps:

### Step 1: Rewrite Cotangent Functions
We can use the identity \( \cot(\theta) = \tan\left(\frac{\pi}{2} - \theta\right) \) to rewrite the cotangent terms:
- \( \cot\left(\frac{7\pi}{16}\right) = \tan\left(\frac{\pi}{2} - \frac{7\pi}{16}\right) = \tan\left(\frac{8\pi}{16} - \frac{7\pi}{16}\right) = \tan\left(\frac{\pi}{16}\right) \)
- \( \cot\left(\frac{15\pi}{16}\right) = \tan\left(\frac{\pi}{2} - \frac{15\pi}{16}\right) = \tan\left(\frac{8\pi}{16} - \frac{15\pi}{16}\right) = \tan\left(-\frac{7\pi}{16}\right) = -\tan\left(\frac{7\pi}{16}\right) \)

Thus, the expression becomes:
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