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

1 Answer
James
May 7, 2018

The answer
[-cosx(cos^2x)]/sin^2x=-cosx*cot^2x−cosx(cos2x)sin2x=−cosx⋅cot2x

Explanation:

show below

cotx (sinx-cscx)cotx(sinx−cscx)

cotx*sinx-cotx*cscxcotx⋅sinx−cotx⋅cscx

cotx=cosx/sinxcotx=cosxsinx

cscx=1/sinxcscx=1sinx

cosx/sinx*sinx-cosx/sinx*1/sinxcosxsinx⋅sinx−cosxsinx⋅1sinx

cosx-cosx/sin^2x=[cosx*sin^2x-cosx]/sin^2x=[-cosx(1-sin^2x)]/sin^2xcosx−cosxsin2x=cosx⋅sin2x−cosxsin2x=−cosx(1−sin2x)sin2x

1-sin^2x=cos^2x1−sin2x=cos2x

[-cosx(cos^2x)]/sin^2x=-cosx*cot^2x−cosx(cos2x)sin2x=−cosx⋅cot2x

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