AP EAMCET · Maths · Trigonometric Equations
Ifsin \(\left(x+\frac{\pi}{3}\right)+\sin \left(x-\frac{\pi}{3}\right)=1\), then the value of \(x\) in the interval \([0, \pi]\)
- A \(\frac{\pi}{2}\)
- B \(\frac{\pi}{3}\)
- C \(0\)
- D \(\frac{\pi}{4}\)
Answer & Solution
Correct Answer
(A) \(\frac{\pi}{2}\)
Step-by-step Solution
Detailed explanation
\(\sin \left(x+\frac{\pi}{3}\right)+\sin \left(x-\frac{\pi}{3}\right)=1\) \(\Rightarrow \quad 2 \sin x \cdot \cos \frac{\pi}{3}=1\) \([\because 2 \sin A \cdot \cos B=\sin (A+B)+\sin (A-B)]\) \(\Rightarrow \quad 2 \sin x \cdot \frac{1}{2}=1\)…
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