How do you prove tan (2x) = (2tan (x) ) / (1-tan² x) ?

Prove tan(2x) = 2tan(x)/ 1- tan² (x)

Answer: LHS = 2tan(x) / 1- tan²(x) = (2tan (x) ) / (1-tan2 x)  = RHS

As we know that tan(A+B) = tanA+tanB/ 1- tan(A)tan(B)

Explanation: Given that LHS = tan(2x) 

Therefore, tan(2x) = tan (x+x)

we know that tan(a+b) = (tan a + tan b) / 1- (tan a .tan b)

using the above formula   we have

tan (2x) =

= tan(x)+ tan(x) / 1- tan(x) tan(x)

= 2tan(x)/ 1- tan²(x)

= RHS

Hence Proved 2tan(x) / 1- tan²(x) = (2tan (x) ) / (1-tan2 x)  LHS=RHS