JEE Main
Exam JEE Main
Subject Mathematics
Chapter Trigonometric Ratios & Identities JEE Main · Mathematics · Trigonometric Ratios & Identities
The number of values of x in the interval [0,3 π] satisfying 2 ^2...
The number of values of
x \mathrm{x} x in the interval
[ 0 , 3 π ] [0,3 \pi] [ 0 , 3 π ] satisfying
2 sin 2 x + 5 sin 2 x − 3 = 0 2 \sin ^2 x+5 \sin ^2 x-3=0 2 sin 2 x + 5 sin 2 x − 3 = 0 is
Step-by-step solution
2 sin 2 x + 5 sin x − 3 = 0 ⇒ ( sin x + 3 ) ( 2 sin x − 1 ) = 0 ⇒ sin x = − 3 or sin x = 1 2 ⇒ no solution or sin x = sin π 6 ⇒ x = n π + ( − 1 ) n π 6 \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} 2 sin 2 x + 5 sin x − 3 = 0 ⇒ ( sin x + 3 ) ( 2 sin x − 1 ) = 0 ⇒ sin x = − 3 or sin x = 2 1 ⇒ no solution or sin x = sin 6 π ⇒ x = nπ + ( − 1 ) n 6 π But
x ∈ [ 0 , 3 π ] x \in[0,3 \pi] x ∈ [ 0 , 3 π ] \Rightarrow x=
π 6 , 5 π 6 , 13 π 6 , 17 π 6 \frac{\pi}{6}, \frac{5 \pi}{6}, \frac{13 \pi}{6}, \frac{17 \pi}{6} 6 π , 6 5 π , 6 13 π , 6 17 π four solution
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