Name: Joshua
Who is asking: Student
Level of the question: All

Question: I'm having trouble proving that cos(3X)=cos cubed X -(cosX)(sin squared X)

 

Joshua,

That's good news because cos(3x) ≠ cos3X - cosX sin2X. What is true is that

cos(3x) = cos3X - 3 cosX sin2X

To prove this I wrote cos(3X) as cos(2X + X) and used the identity that

cos(A + B) = cos A cos B - sin A sin B

In simplifying the expression above I need to use

sin(A + B) = sin A cos B + cos A sin B

Penny