Question

If $5cos2\theta +2co{s}^2\theta /2+1=0,-\pi <\theta <\pi$, then $\theta$-

• A. $\pi /3$
• B. $\pi /3,co{s}^{-1}\left(3/5\right)$
• C. $co{s}^{-1}\left(3/5\right)$
• D. $\pi /3,\pi -co{s}^{-1}\left(3/5\right)$

Answer 1

The correct option is D $\pi /3,\pi -co{s}^{-1}\left(3/5\right)$

$5cos2\theta +2co{s}^2\theta /2+1=0,-\pi <\theta <\pi$
$\Rightarrow 10{\cos }^2\theta +\cos \theta -3=0$
$\Rightarrow \cos \theta =\frac{1}{2}$ and $\cos \theta =-\frac{3}{5}$
$\Rightarrow \cos \theta =\cos \frac{\pi }{3}$ and $\theta ={\cos }^{-1}(-\frac{3}{5})$
$\Rightarrow \theta =\frac{\pi }{3},\theta =\pi -{\cos }^{-1}\left(\frac{3}{5}\right)$