Question

sin 60 = 2 tan 30 / 1 + tan²30​

Answer 1

Answer:

$sin60 = \frac{2tan30}{1 + {tan}^{2} 30} \\ \frac{ \sqrt{3} }{2} = \frac{2 \times \frac{1}{ \sqrt{3} } }{1 + { \frac{1}{ \sqrt{3} } }^{2} } \\ \frac{ \sqrt{3} }{2} = \frac{ \frac{2}{ \sqrt{3} } }{1 + \frac{1}{3} } \\ \frac{ \sqrt{3} }{2} = \frac{ \frac{2}{ \sqrt{} 3} }{ \frac{4}{3} } \\ \frac{ \sqrt{3} }{2} = \frac{2}{ \sqrt{3} } \times \frac{3}{4} \\ \frac{ \sqrt{3} }{2} = \frac{6}{4 \sqrt{3} } \\ 4 \sqrt{3} \times \sqrt{3} = 6 \times 2 \\ 4 \times 3 = 12 \\ 12 = 12 \\ \\ hence \: it \: is \: proved \\ that \: \\ sin60 = \frac{2tan30}{1 + {tan}^{2}30 } \\ \\ or \: \\ it \: is \: equal \: to \: 1$