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Question: Answered & Verified by Expert
If $\sin (2 x)=\frac{\sqrt{5}-1}{4}$ then $x=\frac{n}{2} \pi+(-1)^n(m)$, $n \in \mathbf{Z}$, find $m$.
MathematicsTrigonometric Ratios & IdentitiesAP EAMCETAP EAMCET 2020 (22 Sep Shift 2)
Options:
  • A $\frac{\pi}{10}$
  • B $\frac{\pi}{5}$
  • C $\frac{\pi}{20}$
  • D $\frac{\pi}{40}$
Solution:
1112 Upvotes Verified Answer
The correct answer is: $\frac{\pi}{20}$
$$
\text { } \begin{aligned}
\sin 2 x & =\frac{\sqrt{5}-1}{4} \\
\sin 2 x & =\sin \frac{\pi}{10} \\
2 x & =n \pi+(-1)^n \frac{\pi}{10} \\
x & =\frac{n \pi}{2}+(-1)^n \frac{\pi}{20}
\end{aligned}
$$
but given,
$$
x=\frac{n \pi}{2}+(-1)^n \cdot m
$$
On comparison, we get $m=\frac{\pi}{20}$ Hence, option (3) is correct.

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