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if 2 sin left frac pi 3 2x right 1 0 0 x frac pi 2
Question:
If \( 2 \sin \left( \frac{\pi}{3} - 2x \right) - 1 = 0 \), \( 0<x<\frac{\pi}{2} \), then the value of \( x \) is:
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To solve trigonometric equations, isolate the trigonometric function and use known angle values for sine or cosine.
KEAM - 2024
KEAM
Updated On:
Mar 7, 2025
\( \frac{\pi}{4} \)
\( \frac{\pi}{3} \)
\( \frac{5\pi}{12} \)
\( \frac{\pi}{12} \)
\( \frac{\pi}{6} \)
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The Correct Option is
D
Solution and Explanation
Step 1:
Solve the given equation: \[ 2 \sin \left( \frac{\pi}{3} - 2x \right) = 1 \] \[ \sin \left( \frac{\pi}{3} - 2x \right) = \frac{1}{2} \] The solution to \( \sin \theta = \frac{1}{2} \) is \( \theta = \frac{\pi}{6} \). Thus: \[ \frac{\pi}{3} - 2x = \frac{\pi}{6} \] \[ 2x = \frac{\pi}{6} \] \[ x = \frac{\pi}{12} \]
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