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

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

1.	Find the value of `sin^(2)5^(@)+sin^(2)10^(@)+sin^(2)15^(@)+.............+sin^(2)90^(@)`.
Answer» `sin^(2)5^(@)+sin^(2)10^(@)sin^(2)15^(@)+.............sin^(2)90^(@)`. `=(sin^(2)5^(@)sin^(2)85^(@))+(sin^(2)10^(@)+sin^(2)80^(@))+(sin^(2)15^(@)+sin^(2)75^(@))+(sin^(2)20^(@)+sin^(2)70^(@))+(sin^(2)25^(@)+sin^(2)65^(@))+(sin^(2)30^(@)+sin^(2)60^(@))+` `(sin^(2)35^(@)+sin^(2)55^(@))+(sin^(2)40^(@)+sin^(2)50^(@))+sin^(2)45^(@)+sin^(2)90^(@)` `={sin^(2)5^(@)+sin^(2)(90^(@)-15^(@))}+...................sin^(2)45^(@)+sin^(2)90^(@)` `=(sin^(2)5^(@)+cos^(2)5^(@))+(sin^(2)10^(@)+cos^(2)15^(@))+...................+sin^(2)45^(@)+sin^(2)90^(@)` `=1+1+1+...............` (upto 8 terms) `+((1)/(sqrt(2)))^(2)+1` `=8+(1)/(2)+1=9(1)/(2)`. Hence the required value `=9(1)/(2)`