Thread: 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.

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.
Similarly expand cos(A+B) and add,

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?

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