Trig Help - Need Help Verifying This Identity

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To verify the identity sin x + tan x / 1 + cos x = tan x, the discussion focuses on simplifying the left side. The user suggests multiplying by cos(x)/cos(x) to facilitate the simplification. This leads to the expression (sin x + tan x)(cos x) / (1 + cos x)(cos x), which simplifies to (sin x * cos x + sin x) / (cos x * (1 + cos x)). Further steps are requested to complete the verification process.
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im trying to verify this identity - sin x + tan x / 1 + cos x = tan x - i get lost very easily and need the steps - can anyone help me?
 
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multiply by cos(x)/cos(x)
 
hmm - can you simplify any of it for me in steps?
 
\frac{sin x + tan x}{1+cos x}

\frac{(sin x + tan x)(cos x)}{(1+cos x) (cos x)}

\frac{sin x \cdot cos x + sin x}{cos x (1+cos x)}

can you take it from here?
 

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