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  4. cos (A+B) ⋅ cos (A-B) is given by:

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Q. $\cos (A+B) \cdot \cos (A-B)$ is given by:

Trigonometric Functions

Solution:

$\cos (A+B) \cdot \cos (A-B)=(\cos A \cos B-\sin A \sin B)$
$(\cos A \cos B+\sin A \sin B)$
$=\cos ^{2} A \cos ^{2} B-\sin ^{2} A \sin ^{2} B$
$=\cos ^{2} A(1-\cos A \cos B+\sin A \sin B)$
$=\cos ^{2} A-\cos ^{2} B \sin ^{2} B-\sin ^{2} A \sin ^{2} B$
$=\cos ^{2} A-\sin ^{2} B\left(\cos ^{2} A+\sin ^{2} A\right)=\cos ^{2} A-\sin ^{2} B$