Question

If `sin α = 1/2` then prove that (3 cos α – 4 cos³ α) = 0.

Answer 1

Given: `sin α = 1/2`

To prove: (3 cos α – 4 cos³ α) = 0

Proof:

`sin α = 1/2`

⇒ cos² α = (1 – sin² α)

= `(1 - 1/4)`

= `3/4`

⇒ `cos α = sqrt(3)/2`.

∴ `(3 cos α - 4 cos^3 α) = 3(sqrt(3)/2) - 4(sqrt(3)/2)^3`

= `(3sqrt(3))/2 - 4((3sqrt(3))/8)`

= `(3sqrt(3))/2 - (12sqrt(3))/8`

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

= 0