The expression ^2(A-B)+ ^2 B-2 (A-B) A B is - Vidyadip

MCQ

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 - B
✓
dependent on A
D
independent of A and B

✓

Answer

Correct option: C.

dependent on A

(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.

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