Chapter 3.4, Problem 39P

To determine

To show: The $y=\sin t$ is solution of $y^{″}+\left(k{\sin }^{2}t\right)y^{\prime }+\left(1-k\cos t\sin t\right)y=0$ for any value of the constant k. If $0<k<2$, show that $1-k\cos t\sin t>0\text{ and }k{\sin }^{2}t\ge 0$.