Question

If θ = 30°, verify that: tan2θ = `(2tanθ)/(1 - tan^2θ)`

Answer 1

Given: θ = 30°
L.H.S.
= tan2θ
= tan2 x 30°
= tan60°
= `sqrt(3)`
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))/(2/3)`

= `(2)/sqrt(3) xx (3)/(2)`
= `sqrt(3)`
⇒ L.H.S. = R.H.S.

⇒ tan2θ = `(2tanθ)/(1 - tan^2 θ)`.