Inverse Trigonometric Functions
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Premium Question
Grade 12
Question:
If $\sin^{-1} x + \cos^{-1} y = \frac{2\pi}{5}$, then $\cos^{-1} x + \sin^{-1} y$ equals:
(1) $\frac{\pi}{5}$
(2) $\frac{2\pi}{5}$
(3) $\frac{3\pi}{5}$
(4) $\frac{4\pi}{5}$
Step-by-Step Solution
Key Concept: Add the given equation to ($\cos^{-1} x + \sin^{-1} y$) and use $\sin^{-1} t + \cos^{-1} t = \pi/2$ for both $x$ and $y$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (3)