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!