Question

Without using tables, evaluate the following: 4(sin⁴30° + cos⁴60°) - 3(cos²45° - sin²90°).

Answer 1

4(sin⁴30° + cos⁴60°) - 3(cos²45° - sin²90°).

sin30° = `(1)/(2)`
sin90° = 1

cos45° = `(1)/sqrt(2)`

cos60° = `(1)/(2)`
4(sin⁴30° + cos⁴60°) - 3(cos²45° - sin²90°)

= `4((1/2)^4 + (1/2)^4) -3((1/sqrt(2))^2 - (1)^2)`

= `4(1/16 + 1/16) -3(1/2 - 1)`

= `4 xx (2)/(16) + 3 xx (1)/(2)`

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

= `(4)/(2)`
= 2.