How can i simplify #(sin x + cos x)/(1-tan(-x)#?

1 Answer
Nghi N
May 2, 2017

cos x

Explanation:

Simplify: #f(x) = (sin x + cos x)/(1 - tan (-x))#
Develop the denominator:
#1 - tan (-x) = 1 - sin (-x)/(cos (-x)) = 1 + (sin x)/(cos x)#
because: sin (-x) = - sin x, and cos (-x) = cos x
#1 - tan (-x) = (cos x + sin x)/(cos x)#
Therefore:
#f(x) = ((sin x+ cos x)/(cos x + sin x))(cos x) = cos x#

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