Question

cos^2 9° + cos^2 18° +...........+ cos^2 81° =

Answer 1

cos^2 (90-9)°=sin^2 81°
similarly
cos^2 (90-18)°=sin^2 72°
there are four pair cos^2 a+sin^2 a=1
cos^2 45°= 1/2
ans= 4+1/2= 9/2