First slide

Compound angles

Question

If $(1 + \tan α) (1 + \tan 4 α) = 2$ , $α \in (0, \frac{π}{16})$ then $α =$

Moderate

A

$\frac{π}{20}$
B

$\frac{π}{30}$
C

$\frac{π}{40}$
D

$\frac{π}{60}$

Solution

$\begin{array}{l} If α + β = \frac{π}{4} then \\ (1 + \tan α) (1 + \tan β) = 2 \\ G i v e n (1 + \tan α) (1 + \tan 4 α) = 2 \\ \Rightarrow α + 4 α = \frac{π}{4} \\ \Rightarrow α = \frac{π}{20} \end{array}$

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