1.

`sin^(2)5^@+sin^(2)10^@+sin^(2)15^@ +.......+sin^(2)85^@ + sin^(2)90^@=`

Answer» `sin^2 5^@+sin^2 10^@+sin^2 15^@+...+sin^2 85^@+sin^2 90^@`
`=sin^2 (90-85)^@+sin^2 (90-80)^@+sin^2 (90-75)^@+...sin^2 75^@+ sin^2 80^@+sin^2 85^@+sin^2 90^@`
`=cos^2 85^@ + cos^2 80^@ +cos^2 75^@+...+sin^2 45^@+...+sin^2 75^@+ sin^2 80^@+sin^2 85^@+sin^2 90^@`
`=(cos^2 85^@ + sin^2 85^@) + (cos^2 80^@ + sin^2 80^@) +...(cos^2 40^@ + sin^2 40^@))+sin^2 45^@+sin^2 90^@`
`=1+1+1+1+1+1+1+1+1/2+1`
`=9.5`
`:. sin^2 5^@+sin^2 10^@+sin^2 15^@+...+sin^2 85^@+sin^2 90^@ = 9.5`


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