Question

The value of tan$15^\circ$ + tan$75^\circ$ is equal to

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

Answer 1

Answer: (E)

$\tan 15^{\circ}+\tan 75^{\circ}$
$=\frac{\sqrt{3}-1}{\sqrt{3}+1}+\frac{\sqrt{3}+1}{\sqrt{3}-1}$
$\left[\because \tan 15^{\circ}=\frac{\sqrt{3}-1}{\sqrt{3}+1}, \tan 75^{\circ}=\frac{\sqrt{3}+1}{\sqrt{3}-1}\right]$
$=\frac{(\sqrt{3}-1)^{2}+(\sqrt{3}+1)^{2}}{(\sqrt{3}+1)(\sqrt{3}-1)}$
$=\frac{3+1-2 \sqrt{3}+3+1+2 \sqrt{3}}{3-1}=4$