Question

if $\cos {20}^o=k$ and $\cos x=2k^2-1,$ then the possible values of $x$ between $0^o$ and ${360}^o$ are:

• A. $140^{\circ }$ and $270^{\circ }$
• B. $40^{\circ }$ and $140^{\circ }$
• C. $40^{\circ }$ and $320^{\circ }$
• D. $50^{\circ }$ and $130^{\circ }$

Answer 1

Answer: (C)

We have $k=\cos 20^{\circ }...$(i)
and $2k^2-1=\cos x...$ (ii)
From Eqs.(i) and (ii), we get
$2{\cos }^{2}20^{\circ }-1=\cos x$
$\Rightarrow \cos x=\cos 40^{\circ }$
$\Rightarrow x=40^{\circ }$
or $x=360^{\circ }-40^{\circ }=320^{\circ }$
$\therefore$ The values of $x$ lying between $0^{\circ }$ and $360^{\circ }$ are $40^{\circ }$ and $320^{\circ }$.