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)

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