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The expression cos^(2)(A-B)+cos^(2)B-2...

The expression `cos^(2)(A-B)+cos^(2)B-2cos(A-B)cosAcosB` is

A

dependent on B

B

dependent on A and B

C

dependent on A

D

independent of A and B

Text Solution

Verified by Experts

The correct Answer is:
C
`cos^(2)(A-B)+cos^(2)B-2cos(A-B)`
`cosAcosB=cos^(2)(A-B)+cos^(2)B-cos(A-B){cos(A-B)+cos(A+B)}`
`=cos^(2)B-cos(A-B)cos(A+B)`
`=cos^(2)B-(cos^(2)A-sin^(2)B)`
`=1-cos^(2)A=sin^(2)A`
Hence it depends on A.
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