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Answered 2010-06-17 00:11:40

It's easiest to show all of the work (explanations/identities), and x represents theta.

cosxcotx + sinx = cscx

cosx times cosx/sinx + sinx = csc x (Quotient Identity)

cosx2 /sinx + sinx = csc x (multiplied)

1-sinx2/sinx + sinx = csc x (Pythagorean Identity)

1/sinx - sinx2/sinx + sinx = csc x (seperate fraction)

1/sinx -sinx + sinx = csc x (canceled)

1/sinx = csc x (cancelled)

csc x =csc x (Reciprocal Identity)

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