Question

How do you do,
csc2x-cot2x = tanx

Answer 1

`csc2x-cot2x=tanx \\ \\ ((1)/(2)cscxsecx) -( (cotx-tanx)/(2) )=tanx \\ \\ ((cscxsecx)/(2)) -( (cotx-tanx)/(2) )=tanx \\ \\ (( (1)/(sinx) (1)/(cosx) )/(2)) -( (cotx-tanx)/(2) )=tanx \\ \\ ((1)/(2(sinxcosx))) -( (cotx-tanx)/(2) )=tanx \\ \\ ((1)/(2(sinxcosx))) -( ((sinxcosx)*cotx-tanx)/(2*(sinxcosx)) )=tanx \\ \\ (1-(cos^2x-sin^2x))/(2(sinxcosx)) =tanx \\ \\ (1-cos^2+sin^2x)/(2(sinxcosx))=tanx`


`(sin^2x+sin^2x)/(2(sinxcosx)) =tanx \\ \\ (1-cos2x)/(sin2x) =tanx \\ \\ (sin2x)/(cos2x+1)=tanx \\ \\ tanx=tanx`