Given sin(θ+α)/cos(θ-α)=1-m/1+m
Prove that tan(π/4-θ)tan(π/4-α)=m
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2 Answers
2305\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)
Himanshu Giria In the second last step shouldn't it be tan a in 1 of the denominator
Upvote·0· Reply ·2013-08-08 20:34:50
1357Componendo & Dividendo should do..
- Harsh Jaiswal No sir i tried it but did not work