# Compound Angle Formula.

• Mar 20th 2010, 12:25 AM
Tina7906
Compound Angle Formula.
I just started learning Trig identities and i've never been so confused in my life! Can someone please explain how to do this?

Prove: cos (A-B) - cos (A+B) = 2sin (A) sin (B)

Thanks.
• Mar 20th 2010, 01:40 AM
sa-ri-ga-ma
Quote:

Originally Posted by Tina7906
I just started learning Trig identities and i've never been so confused in my life! Can someone please explain how to do this?

Prove: cos (A-B) - cos (A+B) = 2sin (A) sin (B)

Thanks.

Hi, Tina, welcome to MHF,
According to the compound angle formula expand
cos(A-B) = cosA*cosB +sinA*sinB.
• Mar 20th 2010, 02:03 AM
Tina7906
Thank you!

I did that at first and that's where i got stuck.
Im not actually sure how to add and make it equal 2sin (A) sin (B).

Would you be able to explain further?
• Mar 20th 2010, 04:13 AM
sa-ri-ga-ma
Quote:

Originally Posted by Tina7906
Thank you!

I did that at first and that's where i got stuck.
Im not actually sure how to add and make it equal 2sin (A) sin (B).

Would you be able to explain further?

cos(A+B) = cosA*cosB -sinA*sinB
cos(A-B) = cosA*cosB + sinA*sinB
So
cos(A-B) - cos(A+B) = 2sinA*sinB