SOLUTION: Prove using reciprocal and pythagorean identities: (cscx-cotx)/(secx-1)= cotx I have already done: ((1/sinx)-(cosx/sinx))/((1/cosx)-1))= ((1-cosx)/sinx))/((1-cosx)/(cosx))= ((1

Question 826390: Prove using reciprocal and pythagorean identities: (cscx-cotx)/(secx-1)= cotx
I have already done:
((1/sinx)-(cosx/sinx))/((1/cosx)-1))=
((1-cosx)/sinx))/((1-cosx)/(cosx))=
((1-cosx)/sinx))*((cosx)/(1-cosx))=
((1-cosx)cosx))/((sinx(1-cosx))=
((cosx-(cos^2))/(sinx-sinxcosx)
This is where is get stuck...
Thank you
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
You're going to laugh (or cry) when you see how close you were:

We're going to reduce this fraction. And since only factors cancel, we will factor the numerator and denominator:

And, as we can see, a factor will cancel:

leaving

which is equal to:

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