How do you prove that $(cos(2x) + sin^2x)/cosx = cosx$ ?

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Answer 1 · 2017-04-08T22:54:26

Multiply by $cos(x)$

$cos(2x) + 1 - cos^2(x) = cos^2(x)$
implies
$cos(2x) = 2cos^2(x) - 1$
which is true

Answer 2 · 2017-04-08T23:12:58

Here's another way of getting the answer.

Note that $cos^2x+ sin^2x = 1 -> sin^2x = 1- cos^2x$ and that $cos2x = 1 - 2sin^2x$ . Therefore, we have:

$(1 - 2sin^2x + sin^2x)/cosx = cosx$

$(1 - sin^2x)/cosx = cosx$

From above, we can derivative that $cos^2x = 1- sin^2x$ .

$cos^2x/cosx = cosx$

$cosx = cosx$

This has been proved.

Hopefully this helps!

How do you prove that (cos(2x) + sin^2x)/cosx = cosx(cos(2x) + sin^2x)/cosx = cosx?