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# How do you prove tan (2x) = (2tan (x) ) / (1-tan^{2} x) ?

Prove tan(2x) = 2tan(x)/ 1- tan^{2 }(x)

## Answer: LHS = 2tan(x) / 1- tan^{2}(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- tan^{2}(x)

= RHS

### Hence Proved 2tan(x) / 1- tan^{2}(x) = (2tan (x) ) / (1-tan2 x) LHS=RHS

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