Inverse Trigonometric Functions
Inequalities
Premium Question
Grade 12
Question:
The set of all $x$ satisfying $\cos^{-1} x > \sin^{-1} x$ is:
(1) $(-1, \frac{1}{\sqrt{2}})$
(2) $[-1, \frac{1}{\sqrt{2}})$
(3) $(\frac{1}{\sqrt{2}}, 1]$
(4) $[-1, 0)$
Step-by-Step Solution
Key Concept: Replace $\sin^{-1} x = \pi/2 - \cos^{-1} x$ to get $\cos^{-1} x > \pi/4$. $\cos^{-1}$ is a decreasing function — use that to find the range of $x$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)