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)

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