Question

If `sin θ = 1/2` then 4 cos³ θ – 3 cos θ is equal to ______.

Options

• 1

• 7

• –1

• 0

Answer 1

If `sin θ = 1/2` then 4 cos³ θ – 3 cos θ is equal to 0.

Explanation:

4 cos³ θ – 3 cos θ = cos 3θ   ...(Triple-angle identity) 

If `sin θ = 1/2` then `θ = 30^circ (π/6)` or `150^circ ((5π)/6)`   ...(mod 360°)

For both, 3θ = 90° or 450° ≡ 90° and cos 90° = 0. 

So, the expression equals 0.