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Please explain how to solve the above image problem..............,.......

Please explain how to solve the above image problem..............,.......

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Grade:11

1 Answers

Arun
25763 Points
3 years ago
=sin²5+sin²10+sin²15+.......sin²45+...........+sin²75+sin²80+sin²85+sin²90
We know that sin(90-x) =cosx
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 .
For example : sin²5+cos²5=1=sin²10+cos²10=.......sin²40+cos²40
So given changes to
8+sin²45+sin²90
= 8+1/2+1
=9+1/2= 19/2
 

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