15^ =? - Vidyadip

MCQ

$\tan 15^{\circ}=?$

A
$\frac{(\sqrt{2}+1)}{(\sqrt{2}-1)}$
B
$\frac{(\sqrt{3}+1)}{(\sqrt{3}-1)}$
C
$\frac{(\sqrt{3}-1)}{(\sqrt{3}+1)}$
D
$\frac{(\sqrt{2}-1)}{(\sqrt{2}+1)}$

✓

Answer

(c) $\frac{(\sqrt{3}-1)}{(\sqrt{3}+1)}$
Explanation: $\tan 15^{\circ}=\tan \left(45^{\circ}-30^{\circ}\right)=\frac{\tan 45^{\circ}-\tan 30^{\circ}}{1+\tan 45^{\circ} \tan 30^{\circ}}=\frac{\left(1-\frac{1}{\sqrt{3}}\right)}{\left(1+\frac{1}{\sqrt{3}}\right)}=\frac{(\sqrt{3}-1)}{(\sqrt{3}+1)}$

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