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

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

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Answer 1 · 2017-02-21T23:51:38

See explanation...

Explanation:

Use:

$sec x = 1/cos x$

$tan x = sin x/cos x$

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

Then:

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

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

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

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

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

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

1 Answer

Explanation:

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