How do you verify the identity $(sectheta-1)/(1-costheta)=sectheta$ ?

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Answer 1 · 2017-01-17T20:27:02

see below

Left Hand Side:

$(sec theta -1)/(1-cos theta) =( 1/cos theta -1)/(1-cos theta$

$=((1-costheta)/costheta)/(1-costheta)$

$=(1-costheta)/costheta*1/(1-costheta)$

$=cancel(1-costheta)/costheta*1/cancel(1-costheta)$

$=1/cos theta$

$=sec theta$

$:.=$ Right Hand Side

How do you verify the identity (sectheta-1)/(1-costheta)=sectheta(sectheta-1)/(1-costheta)=sectheta?