=sin25+sin210+.......sin245+..........sin285+sin290
sin(90-x) =cosx, sin²(90-x)= cos²x
=sin25+sin210+.......sin245+..........+cos210+cos25+sin290
And sin2x+cos2x= 1
So in given series we get 8 cases where sin2x+cos2x= 1
=8+sin245+sin290
= 8+1/2+1
=9+1/2
= 19/2