What is sec(x)-cos(x) simplified?

1 Answer
KillerBunny
May 15, 2018

#\sin(x)\tan(x)#

Explanation:

Since #sec(x) = 1/cos(x)#, you have

#sec(x)-cos(x) = 1/cos(x)-cos(x) = \frac{1-cos^2(x)}{cos(x)} = \frac{\sin^2(x)}{cos(x)}#

You may rewrite this as

#\frac{\sin^2(x)}{cos(x)} = \sin(x)\frac{sin(x)}{cos(x)}=\sin(x)\tan(x)#

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