Find the lcm of 4 and 4?

lowest common multiple of 4 and 4 is 4

To verify those for alpha and beta, simply substitute the known values:

sin 30° = cos 60° = 1/2

sin 60° = cos 30° = √3/2

cos 90° = sin 0° = 0

sin -30° = -1/2

sin 120° = √3/2

a.

cos 90° = cos 30° cos 60° - sin 30° sin 60°

0 = √3/2 * 1/2 - 1/2 * √3 / 2 = √3/4 - √3/4 = 0

verified

b.

sin -30° = sin 30° cos 60° - cos 30° sin 60°

-1/2 = 1/2 * 1/2 - √3/2 * √3/2 = 1/4 - 3/4 = -2/4 = -1/2

verified

c.

sin 120° = 2 sin 60° cos 60°

√3/2 = 2 * √3/2 * 1/2 = √3/2

verified