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