The left-side will be made equivalent to the right-side

 --------- Converting tan x to 

 ---- Multiplying by LCD, cos x

 ---------- Factoring out GCF, sin x, in numerator

 ------- Cancelling 1 + cos x in numerator and denominator

, or  

 -------- Converting  to tan x

As seen, the left and right sides are congruent, hence the identity has been proven. 

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