Two equations of two S.H.M. are y=a sin (ωt−α) and y=b cos (ωt−α). The phase difference between the two is
y=a sin (ωt−α)=a cos ⎧⎪⎩ωt−α−π2⎫⎪⎭
Another equation is given y=cos (ωt−α)
So, there exists a phase difference of π2=90∘