Question

The value of ${\cos }^2{5}^0+{\cos }^2{10}^0+{\cos }^2{15}^0+{\cos }^2{20}^0+{\cos }^2{70}^0+{\cos }^2{75}^0+{\cos }^2{80}^0+{\cos }^2{85}^0$ is equal to

Answer 1

The value of ${\cos }^2{5}^0+{\cos }^2{10}^0+{\cos }^2{15}^0+{\cos }^2{20}^0+{\cos }^2{70}^0+{\cos }^2{75}^0+{\cos }^2{80}^0+{\cos }^2{85}^0$
$=({\cos }^2{5}^0+{\sin }^2{5}^0)+({\cos }^2{10}^0+{\sin }^2{10}^0)+({\cos }^2{15}^0+{\sin }^2{15}^0)+({\cos }^2{20}^0+{\sin }^2{20}^0)$
$=1+1+1+1=4$
$[\because \cos {85}^0=\cos ({90}^0-5^0)=\sin 5^{0}etc]$