Question

Solve for x:
sin2x=cosx

Answer 1

Applying our Sine Double Angle Formula:\[\Large\rm \color{orangered}{\sin2x=2\sin x \cos x}\]Gives us:\[\Large\rm \color{orangered}{\sin2x}=cosx\]\[\Large\rm \color{orangered}{2\sin x \cos x}=\cos x\]

Answer 2

Subtracting cos x from each side gives us,\[\Large\rm 2\sin x \cos x -\cos x=0\]Factor out a cosx from each term,\[\Large\rm \cos x(2\sin x-1)=0\]Solve for x in each case,\[\Large\rm \cos x=0,\qquad\qquad\qquad 2\sin x-1=0\]