Trigonometrical Equations 3 Question 4
4. The number of values of $x$ in the interval $[0,5 \pi]$ satisfying the equation $3 \sin ^{2} x-7 \sin x+2=0$ is
(1998, 2M)
(a) 0
(b) 5
(c) 6
(d) 10
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Answer:
Correct Answer: 4. (c)
Solution:
- Given, $3 \sin ^{2} x-7 \sin x+2=0$
$\Rightarrow \quad 3 \sin ^{2} x-6 \sin x-\sin x+2=0$
$\Rightarrow \quad 3 \sin x(\sin x-2)-1(\sin x-2)=0$
$\Rightarrow \quad(3 \sin x-1)(\sin x-2)=0$
$\Rightarrow \quad \sin x=\frac{1}{3} \quad[\because \sin x=2$ is rejected $]$
$\Rightarrow \quad x=n \pi+(-1)^{n} \sin ^{-1} \frac{1}{3}, n \in I$
For $\quad 0 \leq n \leq 5, x \in[0,5 \pi]$
There are six values of $x \in[0,5 \pi]$ which satisfy the equation $3 \sin ^{2} x-7 \sin x+2=0$.
