Question

${\cos }^2\frac{3\pi }{5}+{\cos }^2\frac{4\pi }{5}$ is equal to -

• A. $4/5$
• B. $5/2$
• C. $5/4$
• D. $3/4$

Answer 1

Answer: (D)

$3/4$

${\cos }^2\frac{3\pi }{5}+{\cos }^2\frac{4\pi }{5}=1+\frac{1}{2}(\cos \frac{6\pi }{5}+\cos \frac{8\pi }{5})=1+\cos \frac{7\pi }{5}\cos \frac{\pi }{5}=1-\cos \frac{2\pi }{5}\cos \frac{\pi }{5}=1-\cos {72}^{\circ }\cos {36}^{\circ }$

$=1-(\frac{\sqrt{5}-1}{4})(\frac{\sqrt{5}+1}{4})=1-\frac{1}{4}=\frac{3}{4}$