Question

The expression $co{s}^2(A-B)+co{s}^{2}B-2cos(A-B)cosAcosB$ is independent of

• A. A
• B. B
• C. Both A and B
• D. None

Answer 1

The correct option is B B

The given expression can be written as
$cos(A-B)\left[cos\right(A-B)-2cosAcosB]+co{s}^{2}B=cos(A-B)(cosAcosB+sinAsinB-2cosAcosB)+co{s}^{2}B=cos(A-B)[sinAsinB-cosAcosB)+co{s}^{2}B=-cos(A-B)cos(A+B)+co{s}^{2}B=-(co{s}^{2}A-si{n}^{2}B)+co{s}^{2}B=-co{s}^{2}A+si{n}^{2}B+co{s}^{2}B=-co{s}^{2}A+1=si{n}^{2}A$