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  • If m sin θ = n sin (θ + 2α), then prove that tan (θ + α) cot α = (m + n)/(m – n) [Hints: Express sin(θ + 2α) / sinθ = m/n and apply componendo and dividend]

If m sin \theta = n sin ( \theta + 2 \alpha ), then prove that

tan ( \theta + \alpha ) cot \alpha = (m + n)/(m - n)

[Hints: Express sin( \theta + 2 \alpha ) / sin \theta = m/n and apply componendo and dividend]

Answers (1)

\\Given \ that \ \ m sin \theta =nsin \left( \theta +2 \alpha \right) ~ \\\\ ~~\frac{\sin \left( \theta +2 \alpha \right) }{sin \theta }=\frac{m}{n}~~ \\\\ ~~\frac{\sin \left( \theta +2 \alpha \right) +sin \theta }{\sin \left( \theta +2 \alpha \right) -sin \theta }=\frac{m+n}{m-n}~~~ \\\\

 

\frac{2 \sin \left(\frac{\theta+2 \alpha+\theta}{2}\right) \cdot \cos \left(\frac{\theta+2 \alpha-\theta}{2}\right)}{2 \cos \left(\frac{\theta+2 \alpha+\theta}{2}\right) \cdot \sin \left(\frac{\theta+2 \alpha-\theta}{2}\right)}=\frac{m+n}{m-n}     


   \tan \left( \theta + \alpha \right) .cot \alpha =\frac{m+n}{m-n} \\\\

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infoexpert21

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