If
Then prove that:
Please help me!

 see proof below

Step-by-step explanation:

Given: cos 330 =

Use the Double-Angle Identity: cos 2A = 2 cos² A - 1

Proof LHS → RHS:

LHS                          cos 165

Double-Angle:        cos (2 · 165) = 2 cos² 165 - 1

                             ⇒ cos 330 = 2 cos² 165 - 1

                             ⇒ 2 cos² 165  = cos 330 + 1

Given:                        

Divide by 2:              

Square root:            

Scratchwork:            

             Since cos 165 is in the 2nd Quadrant, the sign is NEGATIVE

LHS = RHS