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JEE Advanced
Exam
JEE Advanced
Subject
Mathematics
Chapter
Trigonometry

JEE Advanced · Mathematics · Trigonometry

Number of solution of the equation ^4 x- ^2 x x+2 ^2 x+ x=0 in 0 ≤...

Number of solution of the equation sin⁡4x−cos⁡2xsin⁡x+2sin⁡2x+sin⁡x=0\sin ^4 x-\cos ^2 x \sin x+2 \sin ^2 x+\sin x=0 in 0≤x≤3π0 \leq x \leq 3 \pi is

Correct answer

4

Step-by-step solution

sin⁡2x[sin⁡2x+sin⁡x+2]=0⇒sin⁡x=0, where x=0,π,2π,3π\begin{aligned} & \sin ^2 x\left[\sin ^2 x+\sin x+2\right]=0 \\ & \Rightarrow \sin x=0, \text { where } x=0, \pi, 2 \pi, 3 \pi\end{aligned}
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