Q. If $\cos{20{^\circ} = k}$ and $cos\ x = 2k^{2} - 1$, then the possible values of $x$ between $0{^\circ}$ and $360{^\circ}$ are
A) $140{^\circ}$ and $270{^\circ}$
B) $40{^\circ}$ and $140{^\circ}$
C) $40{^\circ}$ and $320{^\circ}$
D) $50{^\circ}$ and $130{^\circ}$
Explanation
(c)
Given, $k = \cos{20{^\circ}}$
And $2k^{2} - 1 = \cos x$
$\therefore\ 2\cos^{2}{20{^\circ} - 1} = \cos x$
$\Rightarrow \ \cos{x = \cos{40{^\circ}}}$
$\Rightarrow \ \ x = 40{^\circ}$
or $x = 360{^\circ} - 40{^\circ} = 320{^\circ}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.