How do you simplify the expression $secxcotx-cotxcosx$ ?

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Answer 1 · 2016-08-28T02:00:33

$secxcotx - cotxcosx=sinx$ for all $x$ such that $cosx, sinx != 0$

We will use the following:

$secxcotx - cotxcosx = 1/cosx*cosx/sinx - cosx/sinx*cosx$

$=1/sinx-cos^2x/sinx$ (assuming $cosx != 0$ )

$=(1-cos^2x)/sinx$

$=sin^2x/sinx$

$=sinx$ (assuming $sinx != 0$ )

How do you simplify the expression secxcotx-cotxcosxsecxcotx-cotxcosx?