Ive been working on this problem for quite some time now and i haven't been able to figure it out.

tanU(cscU-sinU)=cosU

this is what ive done so far

tanU*cscU - tanU*sinU

(sinU/cosU)*(1/sinU) - (sinU/cosU)*sinU

(1/cosU) - (sin^2U/cosU)

(1-sin^2(U)/cosU)

Half Angles Formula

(1-1+cos(2U))/2cosU

cos(2U)/2cosU

Double angles Formula

(2cos^2(U)-1)/2cosU

cosU-1

cosU-1 =/= cosU

ands so i end up with that pesky -1 out there.

so what am i doing wrong?