Question

Evaluate the following

cos² 30° + cos² 45° + cos² 60° + cos² 90°

Answer 1

cos² 30° + cos² 45° + cos² 60° + cos² 90°  ....(i)

By trigonometric ratios we have

`cos 30^@ = sqrt3/2    cos 45^@ = 1/sqrt2`

`cos 60^@ = 1/2    cos 90^@ = 0`

By substituting above values in (i), we get

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

`3/4 +1/2 + 1/4 = 0 => 1 + 1/2 = 3/2`