SOLUTION: Establish the following identity: cos(A+B)cos(A-B)=cos^2(A)+cos^2(B)-1

Algebra ->  Trigonometry-basics -> SOLUTION: Establish the following identity: cos(A+B)cos(A-B)=cos^2(A)+cos^2(B)-1      Log On


   

Question 1131550: Establish the following identity:
cos(A+B)cos(A-B)=cos^2(A)+cos^2(B)-1
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
cos%28A%2BB%29cos%28A-B%29=cos%5E2%28A%29%2Bcos%5E2%28B%29-1+
start with left side:

cos%28A%2BB%29cos%28A-B%29

=

=

=

=cos%5E2%28A%29+cos%5E2%28B%29+-+sin%5E2%28A%29+sin%5E2%28B%29%29..............since sin%5E2%28A%29=1-cos%5E2%28A%29 and sin%5E2%28B%29=1-cos%5E2%28B%29, we have

=cos%5E2%28A%29+cos%5E2%28B%29+-+%281-cos%5E2%28A%29%29+%281-cos%5E2%28B%29%29

=

=

=

=+-++1%2Bcos%5E2%28B%29%2Bcos%5E2%28A%29 rearrange the terms

=cos%5E2%28A%29%2Bcos%5E2%28B%29-++1+-> identity is proven