Trigonometry help ! Please ! 10 Points !

This is the hardest thing in the world to me i have been trying for like 20 minuets and I am so irritated. Verify : cos3B = cos^3B-3sin^2BcosB

B= beta

L.H.S
=cos3B
=cos(2B+B)
=cos2BcosB-sin2BsinB
=(2cos²B-1)cosB -(2sinBcosB)sinB
=(cos³B -2sin²BcosB) -(cos³B-cosB+sin²BcosB)
=(cos³B-2sin²BcosB) -cosB[1-(sin²B+cos²B)]
=(cos³B-2sin²BcosB) -(1-1)cosB
=cos³B-2sin²BcosB
R.H.S

Now this would be your easiest one.