Question

if tan A=8/7 then verify that (1+sinA)(1-sinA)/(1+cosA)(1-cosA)=cot^2A

Answer 1

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Answer 2

Step-by-step explanation:

$\frac{(1 + \sin \alpha )(1 - \sin\alpha ) }{(1 + \cos \alpha ) (1 - \cos\alpha ) } = \cot {}^{2} \alpha \\ \\ \: firstly \: rhs \: = \cot {}^{2} \alpha \\ since \: \:tan \: \alpha = \frac{8}{7} \\ thus \\ \cot {}^{2} \alpha = \frac{49}{64} \\ \\ now \: \: \: \: taking \: \: \: lhs \\ \frac{(1 + \sin \alpha )(1 - \sin \alpha ) }{(1 + \cos\alpha )(1 - \cos\alpha ) } \\ \frac{(1 - { \sin {}^{2} \alpha) } }{(1 - \cos {}^{2} \alpha) } \\ \frac{ \cos {}^{2} \alpha }{ \sin {}^{2} \alpha } \\ \cot {}^{2} \alpha = rhs \: = \frac{49}{64} \: \: \: \: \: proved$

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