Need help on this one!

[jordan83]

cos(alpha-beta)cos(alpha+beta) = cos^2(alpha) - sin^2(beta)

Need to prove them to be equal. Thank you!

 

[Gene]

a=alpha
b=beta
cos(a-b)cos(a+b) =
sum of angles)
cos(-b)=cos(b)
sin(-b)=-sin(b)
cos(a)cos(b)+sin(a)sin(b) *
cos(a)cos(b)-sin(a)sin(b) =
(u+v)(u-v)=u²-v²
cos²(a)cos²(b)-sin²(a)sin²(b)
sin²(u)+cos²(v) = 1
cos²(a)(1-sin²(b))-sin²(b)(1-cos²(a)) =
cos²(a)-sin²(b)cos²(a)-sin²(b)+cos²(a)sin²(b) =
cos²(a)-sin²(b)

 

[jordan83]

more help!

cos(a-b)cos(a+b) + sin(a-b)sin(a+b) = 1-2sin^2(b)

 

[pka]

cos(X)cos(Y)+sin(X)sin(Y)=cos(X−Y)
Let X=a−b & Y=a+b.

 

[jordan83]

Ok. I am still confused on how to solve it. Thanks!