Function `x=Asin^(2)omegat+Bcos^(2)omegat=Csinomegat cos omegat` represents simple harmonic motion,

The function, x=Asin^(2)omegat+Bcos^(2)omegat+Csinomegatcosomegat represents SHM

Funcation x=A sin^(2) omegat+B cos^(2) omegat+ C sin omegat cos omegat Represents SHM.

Show that the equation x- a sin omegat + b cos omegat represents a simple harmonic motion.

What is the time period for the function f(t) = sin omegat + cos omega t may represent the simple harmonic motion ?