Trigonometry question

Question

If tan θ= λtan(A–θ), show that

(λ–1) sinA = (λ+1) sin(2θ–A).

Answer 1

tan θ= λtan(A–θ)

We can rewrite it as

sin θ cos(A–θ) = λcos θ sin(A–θ)

Now expand this expression, regroup, use formulas for sin²θ and cos²θ to reduce to double angle and again regroup. It should be easy. TRY, if any difficulties, let me know.