Question

${\cos }^2{5}^{\circ }+{\cos }^2{10}^{\circ }+{\cos }^2{15}^{\circ }+...+{\cos }^2{85}^{\circ }=$

• A. $8\frac{1}{2}$
• B. $8$
• C. $6$
• D. $9$

Answer 1

Answer: (A)

The correct option is D $8\frac{1}{2}$
$({\cos }^2{5}^{\circ }+{\cos }^2{85}^{\circ })+({\cos }^{2}10+{\cos }^2{80}^{\circ })+\cdot \cdot \cdot +{\cos }^2{45}^{\circ }+\cdot \cdot \cdot$
=$({\cos }^2{5}^{\circ }+{\sin }^2{5}^{\circ })+\left({\cos }^2{10}^{\circ }\right)+\cdot \cdot \cdot +{\cos }^2{45}^{\circ }+\cdot \cdot \cdot [using\cos ({90}^{\circ }-\theta )=\sin \theta ]$
=$1+1+1+\left(8times\right)+\frac{1}{2}=8\frac{1}{2}$