Question

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

• A. Dependent on $B$
• B. Dependent on $A$ and $B$
• C. Dependent on $A$
• D. Independent of $A$ and $B$

Answer 1

Answer: (C)

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