Question

The number of solutions of ${\sin }^2\theta +3\cos \theta =3$ in $[-\pi ,\pi ]$, is

• A. 4
• B. 2
• C. 0
• D. None of these

Answer 1

Answer: (D)

${\sin }^2\theta +3\cos \theta =3$
$\Rightarrow 1-{\cos }^2\theta +3\cos \theta =3$
$\Rightarrow {\cos }^2\theta -3\cos \theta +2=0$
$\Rightarrow (\cos \theta -1)(\cos \theta -2)=0$
$\therefore \cos \theta =1(\because \cos \theta \ne 2)$
$\Rightarrow 0=0^{\circ }$ as $\theta \in [-\pi ,\pi ]$
$\therefore$ The number of solution is 1.