Question

The value of $\tan {15}^o+\tan {75}^o$ is

• A. $2\sqrt{3}$
• B. $2$
• C. $2-\sqrt{3}$
• D. $4\sqrt{3}$
• E. $4$

Answer 1

The correct option is E $4$

The value of $\tan {15}^o+\tan {75}^o$ is
$=\frac{\sqrt{3}-1}{\sqrt{3}+1}+\frac{\sqrt{3}+1}{\sqrt{3}-1}$
$[\because \tan {15}^o=\frac{\sqrt{3}-1}{\sqrt{3}+1},\tan {75}^o=\frac{\sqrt{3}+1}{\sqrt{3}-1}]$
$=\frac{{(\sqrt{3}-1)}^2+{(\sqrt{3}+1)}^2}{(\sqrt{3}+1)(\sqrt{3}-1)}$
$=\frac{3+1-2\sqrt{3}+3+1+2\sqrt{3}}{3-1}=4$