How do you simplify (cos(x))/(sec(x)+tan(x))?

1 Answer
sankarankalyanam
Feb 19, 2018

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

Explanation:

#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#

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