The displacement d of a water wave is given by the equation d = d 0 sin(t + ). Show that this can be written

The displacement d of a water wave is given by the equation d = d₀ sin(ωt + α).  Show that this can be written as d = d₁ sinωt + d₂ cosωt,  where d₁ = d₀ cos α and d₂ = d₀ sin α.