Prove that \(\sin x(\mathrm{cosec}\,x-1)(1+\sin x)=\cos^2x\).[3]
Hence, solve the equation \(\sin2x(\mathrm{cosec}\,2x-1)(1+\sin2x)=1\), for \(0<x<2\pi\) radians. Give your answers in the form \(k\pi\), where \(k\) is a rational number.[5]
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Answer:(a) Identity proved for \(\sin x\ne0\). (b) No solutions to the printed equation.