AP EAMCET · Maths · Trigonometric Equations
The value of \(x\) in \(\left(0, \frac{\pi}{2}\right)\) satisfying the equation \((\sin x)(\cos x)=\frac{1}{4}\) is
- A \(\frac{\pi}{6}\)
- B \(\frac{\pi}{3}\)
- C \(\frac{\pi}{8}\)
- D \(\frac{\pi}{12}\)
Answer & Solution
Correct Answer
(D) \(\frac{\pi}{12}\)
Step-by-step Solution
Detailed explanation
Given, \(\sin x \cos x=\frac{1}{4}\) \(\begin{array}{llll} \Rightarrow & \sin 2 x =\frac{1}{2} \Rightarrow 2 x=30^{\circ}, 150^{\circ} \\ \Rightarrow & x =15^{\circ}, 75^{\circ} \\ \text {or } & x =\frac{\pi}{12}, \frac{5 \pi}{12} \in\left(0, \frac{\pi}{2}\right) \end{array}\)
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