[tex]\because\cos 2x+\sin x=\sin 2x[/tex][tex]\because\sin 2x=2\sin xcosx[/tex][tex]\because\cos 2x=\cos ^2x-\sin ^2x[/tex]
→ Substitute cos 2x and sin 2x by their expressions
[tex]\therefore\cos ^2x-\sin ^2+\sin x=2\sin x\cos x[/tex]
→ Subtract both sides by sin x
[tex]\cos ^2x-\sin ^2x=2\sin xcosx-\sin x[/tex]
→ Take sin x as a common factor in the right side
[tex]\therefore\cos ^2x-\sin ^2x=\sin x(2\cos x-1)[/tex]
From the graph, the equation has 4 solutions, the intersection points between the 2 graphs
