Q. The value of $\cos^{2}{A\ \left( 3 - 4\cos^{2}A \right)^{2} + \sin^{2}{A\ \left( 3 - 4\sin^{2}A \right)^{2}}}$ is equal to
A) $\cos{4A}$
B) $\sin{4A}$
C) 1
D) None of these
Explanation
(c)
$\cos^{2}{A\left( 3 - 4\cos^{2}A \right)^{2} + \sin^{2}{A\left( 3 - 4\sin^{2}A \right)^{2}}}$
$= \left( 3\cos{A - 4\cos^{3}A} \right)^{2} + \left( 3\sin{A - 4\sin^{3}A} \right)^{2}$
$= \left( - \cos{3A} \right)^{2} + \left( \sin{3A} \right)^{2} = 1$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.