Question

Prove that sin 60° = 2 tan 30°/1+ tan² 30°​

Answer 1

◈ LHS :

`:\implies\tt\:sin60\degree`

`:\implies\bf\:(√(3))/(2)`

◈ RHS :

`:\implies\tt\:(2tan30\degree)/(1+tan^230\degree)`

`:\implies\tt\:\frac{2* (1)/(√(3))}{1+{\large(}\frac{1}{{√(3)}}{\large)}^2}`

`:\implies\tt\:(2)/(√(3))* (3)/(3+1)`

`:\implies\tt\:(2)/(√(3))* (3)/(4)`

`:\implies\bf\:(√(3))/(2)`

Hence Proved !!