Trignometry

Given sin(θ+α)/cos(θ-α)=1-m/1+m
Prove that tan(π/4-θ)tan(π/4-α)=m

2 Answers

2305
Shaswata Roy ·

\frac{\sin \theta+\alpha}{\cos \theta-\alpha}=\frac{\sin\theta\cos\alpha+\cos\theta\sin\alpha}{cos\theta\cos\alpha +\sin\theta\sin\alpha}

.\qquad \qquad=\frac{\tan\theta+\tan\alpha}{1+\tan\theta\tan\alpha}=\frac{1-m}{1+m}

m=\frac{1+\tan\theta\tan\alpha-\tan\theta-\tan\alpha}{1+\tan\theta\tan\alpha+\tan\alpha+\tan\alpha}

.\qquad\qquad=\frac{(1-\tan\theta)(1-\tan\alpha)}{(1+\tan\theta)(1+\tan\theta)}=\tan(\pi/4-\theta)\tan(\pi/4-\alpha)

1357
Manish Shankar ·

Componendo & Dividendo should do..

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