MHT CET · Maths · Trigonometric Ratios & Identities
The number of values of \(\mathrm{x}\) in the interval \([0,3 \pi]\) satisfying \(2 \sin ^2 x+5 \sin ^2 x-3=0\) is
- A 1
- B 6
- C 4
- D 2
Answer & Solution
Correct Answer
(C) 4
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & 2 \sin ^2 x+5 \sin x-3=0 \\ & \Rightarrow(\sin x+3)(2 \sin x-1)=0 \\ & \Rightarrow \sin x=-3 \text { or } \sin x=\frac{1}{2} \\ & \Rightarrow \text { no solution or } \sin x=\sin \frac{\pi}{6} \\ & \Rightarrow x=n \pi+(-1) n \frac{\pi}{6}\end{aligned}\)
But \(x \in[0,3 \pi]\)
\(
\Rightarrow x=\frac{\pi}{6}, \frac{5 \pi}{6}, \frac{13 \pi}{6}, \frac{17 \pi}{6}
\)
four solution
But \(x \in[0,3 \pi]\)
\(
\Rightarrow x=\frac{\pi}{6}, \frac{5 \pi}{6}, \frac{13 \pi}{6}, \frac{17 \pi}{6}
\)
four solution
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