How do you simplify #cotx (sinx-cscx)#?

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Answer 1 · 2018-05-07T15:41:04

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#[-cosx(cos^2x)]/sin^2x=-cosx*cot^2x#

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#cotx (sinx-cscx)#

#cotx*sinx-cotx*cscx#

#cotx=cosx/sinx#

#cscx=1/sinx#

#cosx/sinx*sinx-cosx/sinx*1/sinx#

#cosx-cosx/sin^2x=[cosx*sin^2x-cosx]/sin^2x=[-cosx(1-sin^2x)]/sin^2x#

#1-sin^2x=cos^2x#

#[-cosx(cos^2x)]/sin^2x=-cosx*cot^2x#