Question:
Evaluate:
\[
\sec \left( \cos^{-1} \left( \frac{2024}{2025} \right) \right)
\]
Evaluate:
\[
\sec \left( \cos^{-1} \left( \frac{2024}{2025} \right) \right)
\]
Show Hint
To evaluate secant functions, use the identity \( \sec \theta = \frac{1}{\cos \theta} \) and use the given values for \( \cos \theta \) to compute the result.
Updated On: Apr 28, 2025
- \( 2025 \)
- \( 1 \)
- \( \sqrt{2} \)
- \( \frac{2025}{2024} \)
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The Correct Option is A
Solution and Explanation
We start by noting that \( \cos^{-1} \left( \frac{2024}{2025} \right) \) gives an angle \( \theta \) such that:
\[
\cos \theta = \frac{2024}{2025}
\]
Using the identity \( \sec \theta = \frac{1}{\cos \theta} \), we get:
\[
\sec \theta = \frac{1}{\frac{2024}{2025}} = \frac{2025}{2024}
\]
Thus, the value of the expression is \( 2025 \).
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