Prove that: sin(A + B) + sin(A - B)/cos(A+B) = cos(A-B) = tan A ​

Question

Prove that:

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

Answer 1

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

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

⇒ \(\frac{sim(A+B)+sin(A-B)}{cos(A+B)+cos(A-B)}\)

= tanA = RHS 

Hence proved.