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

2 Answers

May 22, 2018

See below

Explanation:

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

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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