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  4. The expression cos 2(A-B)+ cos 2 B-2 cos (A-B) cos A cos B is

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Q. The expression $\cos ^{2}(A-B)+\cos ^{2} B-2 \cos (A-B)$ $\cos A \cos B$ is

Trigonometric Functions

Solution:

$\cos ^{2}(A-B)+\cos ^{2} B-2 \cos (A-B) \cos A \cos B$
$=\cos ^{2}(A-B)+\cos ^{2} B-\cos (A-B)\{\cos (A-B)+\cos (A+B)\}$
$=\cos ^{2} B-\cos (A-B) \cos (A+B)$
$=\cos ^{2} B-\left(\cos ^{2} A-\sin ^{2} B\right)=1-\cos ^{2} A$
Hence, it depends on $A$.