Question

The value of sin² 5° + sin² 10° + sin² 15° + … + sin² 85° + sin² 90° is

A. 7

B. 8

C. 9.5

D. 10

Answer 1

Correct option is C. 9.5

=sin²5 + sin²10 + sin²15 +.......sin²45 +...........+ sin²75 + sin²80 + sin²85 + sin²90

We know that sin(90 - x) =cos x

So sin²(90 - x)= cos²x

=sin²5 + sin²10 + sin²15+.......sin²45+...........+cos²15+cos²10+cos²5+sin²90

And sin²x + cos²x= 1

So, in given series on rearranging terms we get 8 cases where sin²x+cos²x= 1

So, given changes to

8 + sin²45 + sin²90

= 9.5