Can someone help me solve this & show the work so i can understand?

[Nina1220]

Verify the identity:

sin4t=4sintcos3t−4sin3tcost

 

[BigBeachBanana]

Verify the identity:

sin4t=4sintcos3t−4sin3tcost

What have you tried? It involves double-angle identities of sin and cos.

 

[Deleted member 4993]

Verify the identity:

sin4t=4sintcos3t−4sin3tcost

Attack the left-hand-side using sin(A-B) = sinA * cosB - sinB * cosA

 

[Dr.Peterson]

Verify 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.

 

[BigBeachBanana]

Using double-angle identities I was able to show that:
[math]\sin(4t)=4\sin(t)\cos^3(t)-4\sin^3(t)\cos(t)[/math]