Question

The sum $\sqrt{\frac{3}{2}+\sqrt{2}}+\sqrt{\frac{3}{2}-\sqrt{2}}$ is equal to

• A. $\tan \frac{\pi }{3}$
• B. $\cot \frac{\pi }{3}$
• C. $\sec \frac{\pi }{3}$
• D. $\sin \frac{\pi }{3}$

Answer 1

Answer: (C)

$x=\sqrt{\frac{3}{2}+\sqrt{2}}+\sqrt{\frac{3}{2}-\sqrt{2}}$
On squaring both the sides, we get
$x^2=\frac{3}{2}+\sqrt{2}+\frac{3}{2}-\sqrt{2}+2\sqrt{\frac{9}{4}-2}=4$
$\Rightarrow x=2=\sec \frac{\pi }{3}$