Trigonometry & Inverse Trigonometry
Inverse Trig Functions
nta_abhyas_2025
Grade 12
Question:
Let $x + \frac{1}{x} = 2, y + \frac{1}{y} = -2$ and $\sin^{-1} \left(\frac{1}{x}\right) + y = mx$, then the value of $m$ is
Step-by-Step Solution
Key Concept: Finding critical points where equality conditions in inverse trigonometric expressions are satisfied
From $x + \frac{1}{2} = 2$, we get $x = 1$. From $y - 1 = -2$ (equality occurs only when $y = -1$), we get $y = -1$. Then $\cos^{-1}y = \pi$ and $\sin^{-1}x + \cos^{-1}y = \frac{\pi}{2} + \pi = \frac{3\pi}{2}$. The slope $m = \frac{3}{2} = 1.5$.
Correct Answer: 1.5