Mark the correct alternative in the following: The value of sin 2 5 ° + sin 2 10 ° + sin 2 15 ° + … + sin 2 85 ° + sin 2 90 ° is

Question

Philoid · Accepted Answer

=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