Solveeit Logo
Login

Question

Question: \[\tan 15{^\circ} =\]...

tan⁡15∘=\tan 15{^\circ} =

A

13\frac{1}{3}

B

3−2\sqrt{3} - 2

C

2−32 - \sqrt{3}

D

None of these

Answer

2−32 - \sqrt{3}

Explanation

Solution

tan⁡15o=tan⁡(45o−30o)\tan 15^{o} = \tan(45^{o} - 30^{o})

=1−1/31+1/3=3−13+1×3−13−1=2−3= \frac{1 - 1/\sqrt{3}}{1 + 1/\sqrt{3}} = \frac{\sqrt{3} - 1}{\sqrt{3} + 1} \times \frac{\sqrt{3} - 1}{\sqrt{3} - 1} = 2 - \sqrt{3}.