Question

If `sqrt(3) tan θ = 3 sin θ`, find the value of sin θ.

Answer 1

`sqrt(3) tan θ = 3 sin θ`

⇒ `sqrt(3) xx (sin θ)/(cos θ) = 3 sin θ`

⇒ `cos θ = sqrt(3)/3`

= `1/sqrt(3)`

∴ `sin θ = sqrt(1 - cos^2θ)`

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

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

= `sqrt(2/3)`