70^ is equal to - Vidyadip

MCQ

$\tan70^{\circ}$ is equal to

A
$\tan20^{\circ}+\tan50^{\circ}$
B
$2\tan20^{\circ}+\tan50^{\circ}$
✓
$\tan20^{\circ}+2\tan50^{\circ}$
D
$2\tan20^{\circ}+2\tan50^{\circ}$

✓

Answer

Correct option: C.

$\tan20^{\circ}+2\tan50^{\circ}$

(C)
$\tan50^{\circ}=\tan\left(70^{\circ}-20^{\circ}\right)=\frac{\tan70^{\circ}-\tan20^{\circ}}{1+\tan70^{\circ}\tan20^{\circ}}$
$\Rightarrow\tan50^{\circ}+\tan70^{\circ}\tan20^{\circ}\tan50^{\circ}$
$\Rightarrow\tan70^{\circ}-\tan20^{\circ}$
$\Rightarrow\tan50^{\circ}+\tan50^{\circ}=\tan70^{\circ}-\tan20^{\circ}$
$\ldots\left[\because\tan70^{\circ}=\cot20^{\circ}\right]$
$\Rightarrow2\tan50^{\circ}+\tan20^{\circ}=\tan70^{\circ}$

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