Q. 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 $B$
Explanation
(c)
We have,
$\cos^{2}{(A - B) + \cos^{2}{B - 2\cos{(A - B)\cos{A\cos B}}}}$
$= \cos^{2}{(A - B) + \cos^{2}{B - \cos{(A - B) \times \left\lbrack \cos{(A - B) + cos(A + B)} \right\rbrack}}}$
$= \cos^{2}{B - \cos{(A - B)\cos{(A + B)}}}$
$= \cos^{2}{B - (\cos^{2}{A - \sin^{2}B})}$
$= 1 - \cos^{2}{A = \sin^{2}A}$
Hence, it depends on $A$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.