How do you verify the identity $costheta/(1+sintheta)+tantheta=sectheta$ ?

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Answer 1 · 2016-10-03T18:54:59

see below

$cos theta/(1+sin theta) + tan theta = sec theta$

Left Side $=cos theta/(1+sin theta) + tan theta$

$=(cos theta/(1+sin theta))*(1-sintheta)/(1-sin theta) + sin theta/cos theta$

$=(costheta(1-sintheta))/(1-sin^2theta)+sin theta/cos theta$

$=(costheta(1-sintheta))/cos^2theta +sintheta/costheta$

$=(1-sintheta)/cos theta +sintheta/costheta$

$=(1-sintheta+sintheta)/cos theta$

$=1/cos theta$

$=sec theta$

$=$ Right Side

How do you verify the identity costheta/(1+sintheta)+tantheta=secthetacostheta/(1+sintheta)+tantheta=sectheta?