Question

If sin θ = `1/2` and θ is acute, then (3 cos θ – 4 cos³ θ) is equal to ______.

Options

• 0

• `1/2`

• `1/6`

• – 1

Answer 1

If sin θ = `1/2` and θ is acute, then (3 cos θ – 4 cos³ θ) is equal to 0.

Explanation:

We have, sin θ = `1/2`

`\implies` θ = 30°

Now, 3 cos θ – 4 cos³ θ

= 3 cos 30°  – 4 cos³ 30°

= `3 xx sqrt(3)/2 - 4 xx (sqrt(3)/2)^3`

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

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

= 0