First slide

Compound angles

Question

If $α = \frac{π}{14}$ then the value of $(\tan αtan 2 α + \tan 2 αtan 4 α + \tan 4 αtan α)$ is

Easy

A

1
B

$\frac{1}{2}$
C

2
D

$\frac{1}{3}$

Solution

$α + 2 α + 4 α = 7 α = \frac{π}{2}$
$∴ \tan α \cdot \tan 2 α + \tan 2 α \cdot \tan 4 α + \tan α \cdot \tan 4 α = 1$

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