Trigonometrical Equations 3 Question 2
2. The number of solutions of the pair of equations $2 \sin ^{2} \theta-\cos 2 \theta=0$ and $2 \cos ^{2} \theta-3 \sin \theta=0$ in the interval $[0,2 \pi]$ is
(a) 0
(b) 1
(c) 2
(d) 4
(2007, 3M)
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Answer:
Correct Answer: 2. (c)
Solution:
- $2 \sin ^{2} \theta-\cos 2 \theta=0$
$\Rightarrow \quad \sin ^{2} \theta=\frac{1}{4}$
Also, $\quad 2 \cos ^{2} \theta=3 \sin \theta$
$\therefore \sin \theta=\frac{1}{2}$
$[\because \sin \theta+2 \neq 0]$
$\Rightarrow$ Two solutions exist in the interval $[0,2 \pi]$.
