If tanA = tanB, prove that sin(A-B)/sin(A+B) = x-1/x+1

Question

If tanA = tanB, prove that \(\frac{sin(A- B)}{sin(A+B)}\) = \(\frac{x-1}{x+1}\)

Answer 1

Given tanA = x tanB

LHS \(\frac{sin(A- B)}{sin(A+B)}\)

We know that sin(A ±B) = sinA cosB ± cosA sinB

Dividing numerator And denominator by cosA cosB,

= RHS 

Hence, proved.