1. start with the more complicate looking side
2. change everything to sines and cosines, unless I recognize an obvious identity
I will do #2 for you
LS = (tanx + sinx)/(1 + cosx)
= (sinx/cosx + sinx)/(1+cosx)
= [( sinx + sinxcosx)/cosx ]/(1+cosx)
by "obvious identity" I notice in #4 that we have the expression
1 + tan^2x
from the Pythagorean identities
1 + tan^2x = sec^2x
LS = tan^2x/(1+tan^2)
= tan^2x cos^2x
= sin^2x/cos^2x (cos^2x) = sin^2x
= 1 - cos^2x
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