Question

Evaluate the following:

`(3 sin 30° - 4 sin^3 30°)/(2 sin^2 50° + 2 cos^2 50°)`

Answer 1

`(3 sin 30° - 4 sin^3 30°)/(2 sin^2 50° + 2 cos^2 50°)`

= `(3 xx 1/2 - 4(1/2)^3)/(2(sin^2 50+cos^2 50))`

= `(3/2 - 4 xx 1/8)/(2(1))`   ....[∵ sin² θ + cos² θ = 1]

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

= `(2/2)/2`

= `1/2`