Question

if sin =30A sin 2A = 2tan A /1+tan 2A

Answer 1

Given:-
a= 30 
sin2A=2tanA/1+tan2A
 
Solution:-A tan2a = tan 60 = √3 
B tan(30) = 1/√3 2tan(30) = 2/√3  
C tan(30) ^2 0.3bar
1-(1/3) 2/3 
B/C 3/√3  
3/√3 * √3/√3 = √3
Therefore the answer is √3

Answer 2

A = 30----(1)
lhs = sin 2A

= sin 2*30
= sin 60
=√3/2

rhs = (2tan A) / (1+ tan²A)

= (2 tan 30) / (1+ tan² 30)

=(2*1/√3) /[ 1+(1/√3)²]
=(2/√3)/(1+1/3]
=(2/√3) / (4/3)
=(2/√3) * (3/4)
=(2*√3*√3)/(√3*2*2)
=√3/2
∴ lhs = rhs