How do you prove $(sec x + tan x) (1 - sin x) = cos x$ $(sec x + tan x)(1 - sin x) = cos x$ ?

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How do you prove $(sec x + tan x) (1 - sin x) = cos x$ $(sec x + tan x)(1 - sin x) = cos x$ ?

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Answer 1 · 2017-02-21T23:51:38

See explanation...

Explanation:

Use:

$sec x = \frac{1}{cos x}$ $sec x = 1/cos x$

$tan x = \frac{sin x}{cos x}$ $tan x = sin x/cos x$

${cos}^{2} x + {sin}^{2} x = 1$ $cos^2 x + sin^2 x = 1$

Then:

$(sec x + tan x) (1 - sin x) = (\frac{1}{cos x} + \frac{sin x}{cos x}) (1 - sin x)$ $(sec x + tan x)(1 - sin x) = (1/cos x + sin x/cos x)(1- sin x)$

$(sec x + tan x) (1 - sin x) = \frac{(1 + sin x) (1 - sin x)}{cos x}$ $color(white)((sec x + tan x)(1 - sin x)) = ((1+sin x)(1- sin x))/cos x$

$(sec x + tan x) (1 - sin x) = \frac{1 - {sin}^{2} x}{cos x}$ $color(white)((sec x + tan x)(1 - sin x)) = (1-sin^2 x)/cos x$

$(sec x + tan x) (1 - sin x) = \frac{{cos}^{2} x}{cos x}$ $color(white)((sec x + tan x)(1 - sin x)) = cos^2 x/cos x$

$(sec x + tan x) (1 - sin x) = cos x$ $color(white)((sec x + tan x)(1 - sin x)) = cos x$

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How do you prove $(sec x + tan x) (1 - sin x) = cos x$ $(sec x + tan x)(1 - sin x) = cos x$ ?

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Explanation:

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How do you prove (secx+tanx)(1−sinx)=cosx(sec x + tan x)(1 - sin x) = cos x ?

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How do you prove $(sec x + tan x) (1 - sin x) = cos x$ $(sec x + tan x)(1 - sin x) = cos x$ ?