If sin(x+y)/sin(x-y) = a+b/a-b, show that tanx/tany = a/b. ​

Question

If \(\frac{sin(x + y)}{sin(x-y)}\) = \(\frac{a+b}{a-b}\), show that \(\frac{tanx}{tany}\) = \(\frac{a}{b}\).

Answer 1

Given  \(\frac{sin(x + y)}{sin(x-y)}\) = \(\frac{a+b}{a-b}\) 

LHS = \(\frac{sin(A + B)+sin(A-B)}{cos(A+B)+cos(A-B)}\)

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

= tanA = RHS