Question

If θ = 30°, verify that: sin2θ = `(2tanθ)/(1 ++ tan^2θ)`

Answer 1

Given: θ = 30°
L.H.S.
= sin2θ
= sin2 x 30°
= sin60°
= `sqrt(3)/(2)`
R.H.S.
= `(2tanθ)/(1 + tan^2θ)`

= `(2tan30°)/(1 + tan^2 30°)`

= `(2 xx 1/sqrt(3))/(1 + (1/sqrt(3))^2`

= `(2/sqrt(3))/(1 + 1/3)`

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

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

= `sqrt(3)/(2)`
⇒ L.H.S. = R.H.S.

⇒ sin2θ = `(2tanθ)/(1 + tan^2 θ)`.