Problem
Evaluate: \( \sin\left(\sin^{-1}\left(\frac{7}{25}\right)\right) \)
Solution
We use the basic identity:
\[ \sin(\sin^{-1}x) = x \]
Applying this identity:
\[ \sin\left(\sin^{-1}\left(\frac{7}{25}\right)\right) = \frac{7}{25} \]
Final Answer
\[ \boxed{\frac{7}{25}} \]
Explanation
The sine function and its inverse cancel each other when applied in this form, provided the value lies within the domain of the inverse sine function (which is true for \( \frac{7}{25} \)).