How do you prove (cosx/1+sinx)=secx-tanx?

1 Answer
Sean
Mar 5, 2018

Please see below.

Explanation:

.

#cosx/(1+sinx)=secx-tanx#

Let's multiply both the numerator and the denominator by #1-sinx#:

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

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