Question

Value of ${\cos }^2{5}^{\circ }+{\cos }^2{10}^{\circ }+{\cos }^2{80}^{\circ }+{\cos }^2{85}^{\circ }$ is

• A. $1$
• B. $0$
• C. $2$
• D. $3$

Answer 1

Answer: (C)

$2$

${\cos }^{2}5°+{\cos }^{2}10°+{\cos }^{2}80°+{\cos }^{2}85°$

$={\cos }^2(90°-65°)+{\cos }^2(90°-80°)+{\cos }^{2}80°+{\cos }^{2}85°$

$={\sin }^{2}85°+{\cos }^{2}85°+{\sin }^{2}80°+{\cos }^{2}80°$

$=1+1$

$=2$

Hence, the answer is $2.$