Question

Evaluate the value of $\tan 105°$

Answer 1

We have to find the value of $\tan 105°$

$\tan 105°$ can be expressed as

$\tan 105°=\tan (60°+45°)$

We know that

$\tan (A+B)=\frac{\tan A+\tan B}{1-\tan A\times \tan B}$

$\Rightarrow \tan (60°+45°)=\frac{\tan 60°+\tan 45°}{1-\tan 60°\times \tan 45°}$

As

$\tan 60°=\sqrt{3},\tan 45°=1$

$\Rightarrow \tan (60°+45°)=\frac{\sqrt{3}+1}{1-\sqrt{3}\times 1}=\frac{1+\sqrt{3}}{1-\sqrt{3}}$

Hence, the value of $\tan 105°=\frac{1+\sqrt{3}}{1-\sqrt{3}}$