Question

Evaluate the following

sin² 30° + sin² 45° + sin² 60° + sin² 90°

Answer 1

sin² 30° + sin² 45° + sin² 60° + sin² 90°  .....(1)

`sin 30^@ = 1/2     sin 45^@ = 1/sqrt2`

`sin 60^@ = sqrt3/2   sin 90^@ = 1`

By substituting above values in (i), we get

`= [1/2]^2 + [1/sqrt2]^2 + [sqrt3/2]^2 + [1]^2`

`= 1/4 + 1/2 + 3/4 + 1 => (1 + 3)/4 + (1 + 2)/2`

`=> 1 + 3/2 = (2 + 3)/2 = 5/2`