Question

$\cos^2 \frac{\pi}{12} + \cos^2 \frac{\pi}{4} +\cos^2 \frac{5 \pi}{12} = $

• A. $ \frac{3}{2}$
• B. $ \frac{3 + \sqrt{3} }{2}$
• C. $ \frac{2}{3}$
• D. $ \frac{2}{3 + \sqrt{3} }$

Answer 1

Answer: (A)

$\cos^2 \frac{\pi}{12} + \cos^2 \frac{\pi}{4} \cos^2 \frac{\pi}{15} $
$= \cos^{2} 15^{\circ} + \left(\frac{1}{\sqrt{2} }\right)^{2} + \cos^{2} 75^{\circ} $
$ = \cos^{2} 15^{\circ} +\sin^{2} 15^{\circ} + \frac{1}{2} = \frac{3}{2} $