Question

prove that:

tan (2 x 30°) = `(2 tan 30°)/(1– tan^2 30°)`

Answer 1

RHS,

`(2 tan^2 30°)/(1 – tan^2 30°) = (2 (1)/sqrt3)/(1– 1/3) = (2/sqrt3)/(2/3) `

= `2/sqrt3 ÷ 2/3`

= `cancel2/sqrt3 xx3/cancel2`

= `3/sqrt3 = (sqrt3 xx (cancelsqrt3))/cancelsqrt3 `

= `sqrt3`

LHS,
tan (2 x 30°) = tan 60° = `sqrt3`
LHS = RHS