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

asked Nov 8, 2021 202k views

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◈ 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 !!

Benwasd answered Nov 11, 2021

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