Answer: A) \( \frac{1}{\sqrt{5}} \)
Solution:
We know the identity for \( \cos 2x \):
\[
\cos 2x = 1 - 2\sin^2 x
\]
Substitute \( \cos 2x = \frac{3}{5} \):
\[
\frac{3}{5} = 1 - 2\sin^2 x
\]
Rearrange to solve for \( \sin^2 x \):
\[
2\sin^2 x = 1 - \frac{3}{5} = \frac{2}{5}
\]
\[
\sin^2 x = \frac{1}{5}
\]
Taking the square root (since \( x \) is in the first quadrant, \( \sin x > 0 \)):
\[
\sin x = \frac{1}{\sqrt{5}}
\]
Final Answer:
- \( \sin x = \frac{1}{\sqrt{5}} \), so the correct option is \( \text{A} \).
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