First slide

Trigonometric transformations

Question

If $α = \frac{2 π}{7}$ , then $\tan α \tan 2 α + \tan 2 α \tan 4 α + \tan 4 α \tan α =$

Moderate

A

-7
B

5
C

6
D

-5

Solution

$\sum \tan α . t a n 2 α = 1 - \frac{1}{\cos α . \cos 2 α . \cos 4 α}$
$= 1 - \frac{(8) . \sin α}{\sin 8 α} = - 7$

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