AP EAMCET · Maths · Trigonometric Equations
The sum of the solutions of \(\cos x \sqrt{16 \sin ^2 x}=1\) in \((0,2 \pi)\) is
- A \(2 \pi\)
- B \(\frac{13 \pi}{2}\)
- C \(\frac{17 \pi}{4}\)
- D \(4 \pi\)
Answer & Solution
Correct Answer
(D) \(4 \pi\)
Step-by-step Solution
Detailed explanation
\(\cos x \sqrt{16 \sin ^2 x}=1 \Rightarrow 4 \cos x |\sin x|=1\) Case 1: \(\sin x>0 \text{ for } x \in (0, \pi)\) \(4 \cos x \sin x=1 \Rightarrow 2 \sin(2x)=1 \Rightarrow \sin(2x)=\frac{1}{2}\)…
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