Question

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

Answer 1

Answer:

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Answer 2

◈ LHS :

$:\implies\tt\:sin60\degree$

$:\implies\bf\:\dfrac{\sqrt{3}}{2}$

◈ RHS :

$:\implies\tt\:\dfrac{2tan30\degree}{1+tan^230\degree}$

$:\implies\tt\:\dfrac{2\times \dfrac{1}{\sqrt{3}}}{1+{\large(}\dfrac{1}{{\sqrt{3}}}{\large)}^2}$

$:\implies\tt\:\dfrac{2}{\sqrt{3}}\times \dfrac{3}{3+1}$

$:\implies\tt\:\dfrac{2}{\sqrt{3}}\times \dfrac{3}{4}$

$:\implies\bf\:\dfrac{\sqrt{3}}{2}$

Hence Proved !!