Inverse Trigonometric Functions
Trigonometric Simplification
Premium Question
Grade 12
Question:
The value of $\cos(2 \cos^{-1} x + \sin^{-1} x)$ at $x = \frac{1}{5}$ is:
(1) $\frac{2\sqrt{6}}{5}$
(2) $-\frac{2\sqrt{6}}{5}$
(3) $\frac{\sqrt{6}}{5}$
(4) $-\frac{\sqrt{6}}{5}$
Step-by-Step Solution
Key Concept: Rewrite as $\cos(\cos^{-1} x + \pi/2)$ using $\cos^{-1} x + \sin^{-1} x = \pi/2$. Then apply the compound angle formula.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)