First slide

Multiple and sub- multiple Angles

Question

The value of $\cot θ - \tan θ - 2 \tan 2 θ - 4 \tan 4 θ - 8 \cot 8 θ$ is

Moderate

A

0
B

1
C

-1
D

none of these

Solution

We know that
$\begin{array}{l} ∴ \cot α - \tan α = 2 \cot 2 α \\ \cot θ - \tan θ - 2 \tan 2 θ - 4 \tan 4 θ - 8 \cot 8 θ \\ = 2 \cot 2 θ - 2 \tan 2 θ - 4 \tan 4 θ - 8 \cot 8 θ \\ = 2 (2 \cot 4 θ) - 4 \tan 4 θ - 8 \cot 8 θ \\ = 4 \cot 4 θ - 4 \tan 4 θ - 8 \cot 8 θ \\ = 4 (\cot 4 θ - \tan 40) - 8 \cot 8 θ \\ = 4 \times 2 \cot 8 θ - 8 \cot 8 θ = 0 \end{array}$

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