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

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Answer 1 · 2016-09-06T13:57:34

LHS:

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

$=sintheta/((sin theta - costheta)/sintheta) + costheta/((costheta - sin theta)/costheta)$

$=(sinthetasintheta)/(sin theta - costheta) + (costhetacostheta)/(costheta - sintheta)$

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

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

$=((costheta + sin theta)(costheta - sin theta))/(costheta - sin theta)$

$=((costheta + sin theta)cancel(costheta - sin theta))/cancel(costheta - sin theta)$

$=costheta + sintheta$

$LHS = RHS$

Hopefully this helps!

How do you verify the identity sintheta/(1-cottheta)+costheta/(1-tantheta)=sintheta+costhetasintheta/(1-cottheta)+costheta/(1-tantheta)=sintheta+costheta?