Question

sin60 = 2tan30/1+tan²30
@give answer fast@​

Answer 1

i hopE it will help you

Step-by-step explanation:

2 tan 30 /1

Answer 2

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$\mathtt{\huge{\underline{\red{Answer\: :}}}}$

$\: \: \large \orange{ \bold{ \underline{step \: by \: step \: explaination}}}$

$\implies \displaystyle \sf \: sin2 \theta = \frac{2tan \theta}{1 + {tan}^{2} \theta}$

$\implies \displaystyle \sf \: \: lhs \: \: : sin60 \degree= \frac{ \sqrt{3} }{2}$

$\: \implies \displaystyle \sf \: rhs : \frac{2tan30 \degree}{1 + {tan}^{2} 30 \degree}$

$\: \: \implies \displaystyle \sf \: \frac{2 \times \frac{1}{ \sqrt{3} } }{1 + \frac{1}{3} }$

$\: \implies \displaystyle \sf \: \frac{ \frac{2}{ \sqrt{3} } }{\frac{1 + 3}{3} } = \frac{2}{ \sqrt{3} } \times \frac{3}{4}$

$\: \: \implies \displaystyle \sf {\cancel \frac{2}{ \sqrt{3} } \times \cancel\frac{3}{4} }$

$\: \: \implies \displaystyle \sf \: \frac{ \sqrt{3} }{2} \to \: rhs$

$\: \: \boxed{ \underline { \bf{lhs = rhs}}}$

$\: \: \\ \implies \displaystyle \sf{sin60 \degree = \frac{2tan30 \degree}{1 + {tan}^{2} 30 \degree } = \frac{ \sqrt{3} }{2} }$