Find the value of `sin^(2)5^@+sin^(2)10^@+sin^(2)15^@ +.......+sin^(2)85^@ + sin^(2)90^@=`

Options

A. 8
B. 9
C. 8.5
D. 9.5

Answer

D

Explanation

`sin^2 5+sin^2 10+sin^2 15+sin^2 20+...+sin^2 90`


=`(sin^2 5 +sin^2 85)+(sin^2 10 +sin^2 80)+...+sin^2 45 +sin^2 90)`


`=(sin^2 5 +cos^2 85)+(sin^2 10 +cos^2 80)+...+sin^2 45 +cos^2 90`


`=1+1+1+1+1+1+1+1+1/2+1`


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