Question

Sum of sin^2(0)+sin^2(1)+sin^2(2)+...+sin^2(90) = ?

Answer 1

how about using some symmetry ?

Answer 2

\(\large \sin \theta = \cos(90 - \theta )\)

Answer 3

sin^2(0)+sin^2(1)+sin^2(2)+...+sin^2(90)

`sin^2(0) + sin^2(90)` + `sin^2(1) + sin^2(89)` + ...

Answer 4

how to calculate sin^2(1)+sin^2(89)..? (identity?)

Answer 5

sin(89) = sin(90-1) = cos(1)

Answer 6

use sin^2x + cos^2x = 1