Question

if theta=30°,verify that (1) sin 2theta=2tan theta /1+tan²theta​

Answer 1

Step-by-step explanation:

$\alpha = 30 \\ \sin(2 \alpha ) = \sin(2 \times 30) = \sin(60) = \frac{ \sqrt{3} }{2} \\ \frac{2 \tan( \alpha ) }{1 + { \tan}^{2} \alpha } = \frac{2 \tan(30) }{1 + { \tan }^{2} 30} = \frac{2 \times \frac{1}{ \sqrt{3} } }{1 + { (\frac{1}{ \sqrt{3} } )}^{2} } = \frac{ \frac{2}{ \sqrt{3} } }{1 + \frac{1}{3} } = \frac{ \frac{2}{ \sqrt{3} } }{ \frac{3 + 1}{3} } = \frac{2}{ \frac{4}{ \sqrt{3} } } = 2 \times \frac{ \sqrt{3} }{4} = \frac{ \sqrt{3} }{2}$

Hence verified.

Answer 2

Hope you understand