Inverse Trigonometric Functions
Trigonometric Transformations
Premium Question
Grade 12
Question:
A value of $x$ satisfying $\sin[\cot^{-1}(1 + x)] = \cos[\tan^{-1} x]$ is:
(1) $\frac{1}{2}$
(2) $-1$
(3) $0$
(4) $-\frac{1}{2}$
Step-by-Step Solution
Key Concept: Let $\cot^{-1}(1 + x) = a$ and $\tan^{-1} x = b$. Express $\sin a$ and $\cos b$ in terms of $x$ using right-triangle ratios, then equate.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (4)