15^ = - Vidyadip

MCQ

$\tan 15^{\circ}=$

A
$\frac{1}{3}$
B
$\sqrt{3}-2$
✓
$2-\sqrt{3}$
D
$2+\sqrt{3}$

✓

Answer

Correct option: C.

$2-\sqrt{3}$

(C)
$\tan 15^{\circ}=\tan \left(45^{\circ}-30^{\circ}\right)$
$=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}$
$\ldots\left[\because \tan (A-B)=\frac{\tan A-\tan B}{1+\tan A \tan B}\right]$
$=\frac{\sqrt{3}-1}{\sqrt{3}+1} \times \frac{\sqrt{3}-1}{\sqrt{3}-1}=2-\sqrt{3}$

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