Answer:
sinx
Step-by-step explanation:
(1 -cosx)/(tanx) + (sinx)/(1 +cosx) =
-add the fructions using the common denominator
[(1- cosx)( 1+ cosx) + (sin x) ( tan x) ] / (1+ cos x) (tanx) =
-use that: a²-b²= (a+b) (a-b) so (1- cosx)( 1+ cosx) = 1 - cos²x
and that tanx = sin x/ cosx
[(1- cos²x) + (sinx) ( sinx/cosx) ] / (1+ cos x) (tanx) = =
use that: sin²x+cos²x = 1, so sin²x = 1 - cos²x and then add the fractions
[(sin²x cosx + sin²x)/ cos x ] ·(1/ (1+ cos x) (tanx) ] =
[(sinx (sinx cosx + sinx)/ cos x ] ·(1/ (1+ cos x) (tanx) ] =
[tanx (sinx cosx + sinx) / (1+ cos x) (tanx) ] =
sinx (cosx + 1) / (1+ cos x) =
sinx
