If , prove that = 1 2 [ - ^ -1 ( n-m n+m )…

MATHEMATICS · Subjective · A Level · Mathematics · Trigonometry · Trigonometry

Problem

\frac{m\tan(\alpha-\theta)}{\cos^2\theta}=\frac{n\tan\theta}{\cos^2(\alpha-\theta)}

, prove that

\theta=\frac{1}{2}\left[\alpha-\tan^{-1}\left(\frac{n-m}{n+m}\tan\alpha\right)\right].