First slide

Compound angles

Question

The value of tan 20° + 2 tan 50° - tan 70°, is

Moderate

A

1
B

0
C

tan 50°
D

none of these

Solution

We have,
$\begin{array}{l} \tan 20^{\circ} + 2 \tan 50^{\circ} - \tan 70^{\circ} \\ = 2 \tan 50^{\circ} - (\tan 70^{\circ} - \tan 20^{\circ}) \\ = 2 \tan 50^{\circ} - \frac{\sin 50^{\circ}}{\cos 70^{\circ} \cos 20^{\circ}} \\ = 2 \tan 50^{\circ} - \frac{2 \sin 50^{\circ}}{2 \sin 20^{\circ} \cos 20^{\circ}} \\ = 2 \tan 50^{\circ} - \frac{2 \sin 50^{\circ}}{\sin 40^{\circ}} \\ = 2 \tan 50^{\circ} - \frac{2 \sin 50^{\circ}}{\cos 50^{\circ}} = 2 \tan 50^{\circ} - 2 \tan 50^{\circ} = 0 . \end{array}$

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