Q. Value of $\cos^{2}{(A - B)} + \cos^{2}{B - 2\cos{(A - B)}\cos{A\cos B}}$ is
A) $\sin A$
B) $\sin^{2}A$
C) $\cos^{2}A$
D) $\cos A$
Explanation
(b)
$\cos^{2}{(A - B) + \cos^{2}{B - 2\cos{(A - B)\cos{A\cos\ B}}}}$
$= \cos^{2}{(A - B) + \cos^{2}{B - \cos{(A - B)\left\lbrack \cos{(A - B} \right) + \cos{(A + B)}\rbrack}}}$
$= \cos^{2}{B - \cos{(A - B)\cos{(A + B)}}}$
$= \cos^{2}{B - (\cos^{2}{A - \sin^{2}{B) = 1 - \cos^{2}{A = \sin^{2}A}}}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.