Q. If $\cos{x + \cos^{2}{x = 1}}$, then the value of $\sin^{12}{x + 3\sin^{10}{x + 3\sin^{8}{x + \sin^{6}{x - 1}}}}$, is equal to
A) 2
B) 1
C) $- 1$
D) 0
Explanation
(d)
$\cos{x + \cos^{2}{x = 1\ \ \Rightarrow \ \cos{x = \sin^{2}x}}}$
Now, $\sin^{12}{x + 3\sin^{10}{x + 3\sin^{8}{x + \sin^{6}{x - 1}}}}$
$= \cos^{6}{x + 3\cos^{5}{x + 3\cos^{4}{x + \cos^{3}{x - 1}}}}$
$= \left( \cos^{2}{x + \cos x} \right)^{3} - 1 = 1 - 1 = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.