According to the question,
m sin θ = n sin (θ + 2α)
To prove:
tan (θ + α)cot α =(m + n)/(m – n)
Proof:
m sin θ = n sin (θ + 2α)
⇒ sin(θ + 2α) / sinθ = m/n
Applying componendo-dividendo rule, we have,
By transformation formula of T-ratios,
We know that,
sin A + sin B = 2 sin ((A+B)/2) cos ((A – B)/2)
And,
sin A – sin B = 2 cos ((A+B)/2) sin ((A – B)/2)
On applying the formula, we get,
Therefore, tan (θ + α) cot α = (m + n)/(m – n)
Hence Proved