Question

Prove that:

4 (sin⁴ 30° + cos⁴ 60°) – 3 (cos² 45° – sin² 90°) = 2

Answer 1

LHS = 4 (sin⁴ 30° + cos⁴ 60°) – 3 (cos² 45° – sin² 90°)

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

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

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

= 2 

RHS = 2

LHS = RHS