What have you tried? It involves double-angle identities of sin and cos.Verify the identity:
sin4t=4sintcos3t−4sin3tcost
Attack the left-hand-side using sin(A-B) = sinA * cosB - sinB * cosAVerify the identity:
sin4t=4sintcos3t−4sin3tcost
Do you mean this, [imath]\sin(4t)=4\sin(t)\cos(3t)−4\sin(3t)\cos(t)[/imath], which you wrote, or [imath]\sin^4(t)=4\sin(t)\cos^3(t)−4\sin^3(t)\cos(t)[/imath], or some combination? Neither of these is valid, so you are clearly being inconsistent in your notation.Verify the identity:
sin4t=4sintcos3t−4sin3tcost