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!