Question

Evaluate the following:

(cos 0° + sin 45° + sin 30°)(sin 90° – cos 45° + cos 60°)

Answer 1

(cos 0° + sin 45° + sin 30°)(sin 90° − cos 45° + cos 60°)   ....(i)

By trigonometric ratios we have

`cos 0^@ = 1, sin 45^@ = 1/sqrt2, sin 30^@ = 1/2, sin 90^@ = 1, cos 45^@ = 1/sqrt2 cos 6062 = 1/2`

By substituting above values in (i), we get

`(1 + 1/sqrt2 + 1/2)(1 - 1/sqrt2 + 1/2)`

`[3/2 + 1/sqrt2 + 1/sqrt2] [3/2 - 1/sqrt2] => [3/2]^2 - [1/sqrt2]= 9/4 - 1/2 = 7/4`