How can i simplify $\frac{sin x + cos x}{1 - tan (- x)}$ $(sin x + cos x)/(1-tan(-x)$ ?

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How can i simplify $\frac{sin x + cos x}{1 - tan (- x)}$ $(sin x + cos x)/(1-tan(-x)$ ?

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Answer 1 · 2017-05-02T12:45:05

cos x

Explanation:

Simplify: $f (x) = \frac{sin x + cos x}{1 - tan (- x)}$ $f(x) = (sin x + cos x)/(1 - tan (-x))$
Develop the denominator:
$1 - tan (- x) = 1 - \frac{sin (- x)}{cos (- x)} = 1 + \frac{sin x}{cos x}$ $1 - tan (-x) = 1 - sin (-x)/(cos (-x)) = 1 + (sin x)/(cos x)$
because: sin (-x) = - sin x, and cos (-x) = cos x
$1 - tan (- x) = \frac{cos x + sin x}{cos x}$ $1 - tan (-x) = (cos x + sin x)/(cos x)$
Therefore:
$f (x) = (\frac{sin x + cos x}{cos x + sin x}) (cos x) = cos x$ $f(x) = ((sin x+ cos x)/(cos x + sin x))(cos x) = cos x$

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How can i simplify $\frac{sin x + cos x}{1 - tan (- x)}$ $(sin x + cos x)/(1-tan(-x)$ ?

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