How do I verify Cosx/1-sinx = 1+sinx/cosx ?

1 Answer
Benjamin R.
Jan 19, 2018

#cosx/(1-sinx)# * #cosx/cosx#= #(cos^2x)/(cosx(1-sinx))#=#(1-sin^2x)/(cosx(1-sinx))#=#((1+sinx)(1-sinx))/(cosx(1-sinx))#= #(1+sinx)/cosx#

Explanation:

First, begin with the left side and multiply it by #cosx/cosx#( which is equal to 1). Then use the pythagorean identity: #cos^2x#=#1-sin^2x#. Expand: #1-sin^2x#=#(1+sinx)(1-sinx)#. Cancel out #(1-sinx)# and there you are!

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