Question

What is the exact value of tan(105°).
o 2+√3
o -2+√3
o 2-√3
o -2-3

Answer 1

Answer:

-2-√3.

Explanation:

$tan(105)=tan(60+45)=\frac{tan60+tan45}{1-tan60*tan45}=\frac{\sqrt{3}+1}{1-\sqrt{3}}= \frac{(\sqrt{3}+1)^2}{(1-\sqrt{3})(1+\sqrt{3})}=-\frac{3+1+2\sqrt{3}}{2}=-2-\sqrt{3}.$