Question

Find the value of $\cos(\sec^{-1}x)$.

Hint:

Inverse trigonometric functions often simplify using reciprocal identities like $\cos(\sec^{-1}x)=1/x$, valid for $|x|\geq 1$.

Answer 1

Step 1: Let \[ \theta = \sec^{-1}x \implies \sec\theta = x \]

Step 2: Use reciprocal identity. \[ \cos\theta = \frac{1}{\sec\theta} = \frac{1}{x} \]

Final Answer: \[ \boxed{\cos(\sec^{-1}x) = \frac{1}{x}} \]