Proof of difference identities for cosine

[PatternSeeker]

Hi,

I am working on proofs of the difference identities for sine, cosine, and tangent.
I am hoping to solve these using a specific diagram (attached).

I was wondering if you could help me with the difference of cosines. Is it possible to derive it using the attached diagram? If so, how could I go about this?

Details and a relevant diagram are attached.

Thanks

 

[chiro]

Hey PatternSeeker.

If you know the difference between the sines, you can use the fact that sin(x) = cos(pi/2 - x) and then get the identities for difference or sum or cosine terms instead of sine terms.

With the tangent, will need to expand and simplify out sin(a+b)/cos(a+b).

 

[PatternSeeker]

Thank you chiro!