Question

Verify the identity. sin 4u = 2 sin 2u cos 2u

Answer 1

This follows directly from the double angle identity for sine,

sin(2u) = 2 sin(u) cos(u)

But supposing that's not known to you, you could use the angle sum identity:

sin(x + y) = sin(x) cos(y) + sin(y) cos(x)

Since 4u = 2u + 2u, we have

sin(4u) = sin(2u + 2u)

sin(4u) = sin(2u) cos(2u) + cos(2u) sin(2u)

sin(4u) = 2 sin(2u) cos(2u)