Question

Choose the correct answers from the alternatives given.
$Si{n}^2{5}^{\circ }+si{n}^2{6}^{\circ }+...........+si{n}^2{84}^{\circ }+si{n}^2{85}^{\circ }$ =?

• A. 39$\frac{1}{2}$
• B. 40$\frac{1}{2}$
• C. 40
• D. 39 $\frac{1}{\sqrt{2}}$

Answer 1

The correct option is B 40$\frac{1}{2}$

sin $({90}^{\circ }-\theta )=cos\theta$
Hennce, sin $({90}^{\circ }-{85}^{\circ })=cos{5}^{\circ }$
sin $({90}^{\circ }-6^{\circ })=cos{6}^{\circ }$
$si{n}^2{5}^{\circ }+si{n}^2{6}^{\circ }+\cdots +si{n}^2{84}^{\circ }+si{n}^2{85}^{\circ }$
= $(si{n}^2{5}^{\circ }+si{n}^2{85}^{\circ })+(si{n}^2{6}^{\circ }+si{n}^2{85}^{\circ })+\cdots +to40terms+si{n}^2{45}^{\circ }$
$(si{n}^2{5}^{\circ }+co{s}^2{5}^{\circ })+(si{n}^2{6}^{\circ }+co{s}^2{6}^{\circ })+\cdots +to40terms+si{n}^2{45}^{\circ }$
$40+\frac{1}{2}=40\frac{1}{2}$