Come si semplifica (cos (x)) / (sec (x) + tan (x))?

#cos x / (sec x + tan x) = cos x / ((1/cos x) + (sin x/ cos x))#

# => cos ^2 x / (1 + sin x) = (1 - sin^2x) / (1 + sin x)#

#=> (cancel(1+ sin x) * (1 - sin x) ) / cancel(1 + sin x)#

#color(purple)(=> 1 - sin x#