Prove the identity.

label Mathematics
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(cosx) / (1+sinx) 

(cosx) / (1-sinx) 

2secx 

Jan 25th, 2015

cos x/(1+sin x) + cos x/(1-sin x)
= [cos x(1-sin x) + cos x(1+sin x)]/ [(1+sin x)(1- sin x)]
= [cos x - cos x.sin x + cos x + cos x.sin x]/[1- sin^2 x]    ( sin^2 + cos^2 =1)
= 2cos x/cos ^2 x
=2/cos x     ( cos x = 1/sec x)
= 2 sec x

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Jan 25th, 2015

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