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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