Step-by-step explanation:
It's given that A = 30° . Lets find the sin , cos & tan of A
⇒ [tex]\sin A=\sin30 = \frac{1}{2}[/tex]
⇒ [tex]\cos A = \cos 30 = \frac{\sqrt{3} }{2}[/tex]
⇒[tex]\tan A = \tan 30 = \frac{1}{\sqrt{3} }[/tex]
Lets solve the LHS (Left Hand Side) :-
[tex]2(\sin A \times \cos A) = 2(\frac{1}{2} \times \frac{\sqrt{3} }{2}) = \frac{\sqrt{3} }{2}[/tex]
Now lets solve the RHS (Right Hand Side) :-
[tex]\frac{2\tan A}{1+\tan ^{2}A } = \frac{2 \times \frac{1}{\sqrt{3} } }{1 + (\frac{1}{\sqrt{3} } )^{2} } = \frac{2}{\sqrt{3} } \div ( 1 + \frac{1}{3} ) = \frac{2}{\sqrt{3} }\div \frac{4}{3} = \frac{2}{\sqrt{3} } \times\frac{3}{4} =\frac{\sqrt{3} }{2}[/tex]
∴ LHS = RHS ( Proved )
