Question

If `sqrt(3) tan θ = 3 sin θ` then (sin²θ – cos²θ) = ?

Options

• `1/3`

• `1/sqrt(3)`

• `sqrt(3)`

• `2/sqrt(3)`

Answer 1

`bb(1/3)`

Explanation:

`sqrt(3) tan θ = 3 sin θ`

⇒ `(sqrt(3) sin θ)/(cos θ) = 3 sin θ`

⇒ `cos θ = sqrt(3)/3 = 1/sqrt(3)`

sin²θ = (1 – cos²θ) 

= `(1- 1/3)`

= `2/3`

∴ `(sin^2θ - cos^2θ) = (2/3 - 1/3)`

= `1/3`