First slide

Trigonometric transformations

Question

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

Moderate

A

1
B

½
C

2
D

⅓

Solution

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

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