Q. The value of $2\cos{x - \cos{3x - \cos{5x\ }}}$is equal to
A) $16\cos^{3}{x\sin^{2}x}$
B) $16\sin^{3}{x{cos^{2}}x}$
C) $4\cos^{3}{x\sin^{2}x}$
D) $4\sin^{3}{x\cos^{2}x}$
Explanation
(a)
$2\cos{x - \cos{3x - \cos{5x = 2\cos{x - 2\cos x\cos{4x}}}}}$
$= 2\cos{x\ (1 - \cos{4x})}$
$= 2\cos{x\ 2\sin^{2}{2x}}$
$= 4{\cos{x(2\sin{x\cos{x)}}}}^{2}$
$= 16\sin^{2}{x\cos^{3}x}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.