Question

Find the value of the following:

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

Answer 1

sin 90° = 1, cos 60° = `1/2`, cos 45° = `1/sqrt(2)`, sin 30° = `1/2`, cos 0° = 1

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

= `(1 + 1/2 +  1/sqrt(2)) xx (1/1 + 1 - 1/sqrt(2))`

= `((2sqrt(2) + sqrt(2) + 2)/(2sqrt(2))) xx ((sqrt(2) + 2sqrt(2) - 2)/(2sqrt(2)))`

= `((3sqrt(2) + 2)/(2sqrt(2))) xx ((3sqrt(2) - 2)/(2sqrt(2)))`

= `((3sqrt(2))^2 - (2)^2)/8`

= `(9(2) - 4)/8`

= `(18 - 4)/8`

= `14/8`

= `7/4`