Question

Evaluate the Following

4(sin⁴ 30° + cos² 60°) − 3(cos² 45° − sin² 90°) − sin² 60°

Answer 1

4(sin⁴ 30° + cos² 60°) − 3(cos² 45° − sin² 90°) − sin² 60°  .....(i)

By trigonometric ratios we have

`sin 30^@ = 1/2        cos 60^@ = 1/2     cos 45^@ = 1/sqrt2     sin 90^@ = 1   sin 60^@ = sqrt3/2`

By substituting above values in (i), we get

`(4[(1/2)^4 + (1/2)^2]) - 3[[1/sqrt2]^2 - 1] - [sqrt3/2]^2`

`4[1/16 + 1/4] - 3[(1 - [sqrt2])/(sqrt2)^2] - 3/4`

`= 1/4 + 1 - 3/4 + 3/2 = 2`