Question:
If \( 2 \sin \left( \frac{\pi}{3} - 2x \right) - 1 = 0 \), \( 0<x<\frac{\pi}{2} \), then the value of \( x \) is:
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.
Updated On: Apr 7, 2026
- \( \frac{\pi}{4} \)
- \( \frac{\pi}{3} \)
- \( \frac{5\pi}{12} \)
- \( \frac{\pi}{12} \)
- \( \frac{\pi}{6} \)
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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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