AP EAMCET · Maths · Trigonometric Ratios & Identities
If \(\sin (2 x)=\frac{\sqrt{5}-1}{4}\) then \(x=\frac{n}{2} \pi+(-1)^n(m)\), \(n \in \mathbf{Z}\), find \(m\).
- A \(\frac{\pi}{10}\)
- B \(\frac{\pi}{5}\)
- C \(\frac{\pi}{20}\)
- D \(\frac{\pi}{40}\)
Answer & Solution
Correct Answer
(C) \(\frac{\pi}{20}\)
Step-by-step Solution
Detailed explanation
\[ \text { } \begin{aligned} \sin 2 x & =\frac{\sqrt{5}-1}{4} \\ \sin 2 x & =\sin \frac{\pi}{10} \\ 2 x & =n \pi+(-1)^n \frac{\pi}{10} \\ x & =\frac{n \pi}{2}+(-1)^n \frac{\pi}{20} \end{aligned} \] but given, \[ x=\frac{n \pi}{2}+(-1)^n \cdot m \] On comparison, we get…
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