Question

Q:-show that $\frac{2tan30}{1 + {tan}^{2}30 }$=sin60
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Answer 1

Answer:

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Answer 2

$\green{\bold{\underline{ ✪ UPSC-ASPIRANT✪ }}}$

$\red{\bold{\underline{\underline{QUESTION:-}}}}$

Q:-show that $\frac{2tan30}{1 + {tan}^{2}30 }$=sin60

$\huge\tt\underline\blue{Answer }$

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⟹$\frac{2tan30}{1 + {tan}^{2}30 }$

$⟹ \frac{2 \times \frac{1}{ \sqrt{3} } }{1 + ( { \frac{1}{ \sqrt{3} }) }^{2} } </p><p>$

$⟹</p><p> \frac{ \frac{2}{ \sqrt{3} } }{1 + \frac{1}{3} }$

$⟹</p><p> \frac{ \frac{2}{ \sqrt{3} } }{ \frac{4}{3} } = \frac{2}{ \sqrt{3} } \times \frac{3}{4}$

$⟹ \frac{2}{ \sqrt{3} } \times \frac{ \sqrt{3} \times \sqrt{3} }{4} = \frac{2 \sqrt{3} }{4} = \frac{ \sqrt{3} }{2} </p><p>$

Hence proved ✓

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