How do I verify the following trigonometric identity? 1+sinx/cosx=cosx/1-sinx

2 Answers
David Chi
May 22, 2018

See below

Explanation:

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

P dilip_k
Jun 28, 2018

#LHS=(1+sinx)/cosx#

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

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

#=(cosx(cancel(1+sinx)))/((cancel(1+sinx))(1-sinx))#

#=cosx/(1-sinx)=RHS#

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