First slide

Multiple and sub- multiple Angles

Question

The value of $\cot \frac{7 π}{16} + 2 \cot \frac{3 π}{8} + \cot \frac{15 π}{16} =$

Moderate

A

4
B

2
C

-2
D

-4

Solution

$\begin{array}{l} \cot \frac{7 π}{16} + 2 \cot \frac{3 π}{8} + \cot \frac{15 π}{16} = \tan (\frac{π}{2} - \frac{7 π}{16}) + 2 \tan (\frac{π}{2} - \frac{3 π}{8}) + c o t (π - \frac{π}{16}) \\ = \tan \frac{π}{16} - \cot \frac{π}{16} + 2 \tan \frac{π}{8} = - 2 \cot \frac{π}{8} + 2 \tan \frac{π}{8} \\ = - 2 (\cot \frac{π}{8} - \tan \frac{π}{8}) = - 2 \cdot 2 \cot \frac{π}{4} = - 4 \end{array}$

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