Question

1.sin^2 5°+sin^2 10°+sin^2 15°+...+sin^2 90°     is?

Answer 1

$Sin^20+sin^25+Sin^210+Sin^215+....+Sin^40+Sin^245\\.\ \ \ +Sin^250+..Sin^285+Sin^290\\\\=(Sin^20+Sin^290)+(Sin^25+Sin^285)+(Sin^210+Sin^280)+....\\.\ \ \ \ \ +(Sin^235+Sin^255)+(Sin^240+Sin^250)+(Sin^245)\\\\=(Sin^20+Cos^20)+(Sin^25+Cos^25)+(Sin^210+Cos^210)+....\\.\ \ \ \ \ +(Sin^235+Cos^235)+(Sin^240+Cos^240)+(Sin^245)\\\\=1+1+1+1...+1+1/2=9.5$