Question

The value of cos–1$\sqrt{\frac{2}{3}}$ – cos–1$\frac{\sqrt{6} + 1}{2\sqrt{3}}$ is equal to –

• A. $\frac{\pi}{12}$
• B. $\frac{\pi}{8}$
• C. $\frac{\pi}{6}$
• D. $\frac{\pi}{3}$

Answer 1

Answer: (C)

$\frac{\pi}{6}$

Answer 2

I = tan–1 $\left( \frac{1}{\sqrt{2}} \right)$– tan–1$\left\{ \frac{\sqrt{12 - ( - 1 + 2\sqrt{6})}}{(\sqrt{6} + 1)} \right\}$

= tan–1 $\left( \frac{1}{\sqrt{2}} \right)$– tan–1$\left( \frac{\sqrt{5 - 2\sqrt{6}}}{\sqrt{6} + 1} \right)$

= tan–1 $\left( \frac{1}{\sqrt{2}} \right)$– tan–1$\left( \frac{\sqrt{3} - \sqrt{2}}{1 + \sqrt{6}} \right)$

= tan–1 $\left( \frac{1}{\sqrt{2}} \right)$– tan–1 $\sqrt{3}$ + tan–1$\sqrt{2}$

= $\frac{\pi}{2}$ – $\frac{\pi}{3}$ = $\frac{\pi}{6}$.