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Q.
The sum $\sqrt{\frac{3}{2}+\sqrt{2}}+\sqrt{\frac{3}{2}-\sqrt{2}}$ is equal to
Continuity and Differentiability
Solution:
$ 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 $
$\Rightarrow x =2=\sec \frac{\pi}{3}$