UPSC NDA 2 2021 Mathematics Solved Paper

Concept:The function $y = \cos^{-1}(\cos x)$ simplifies to a linear expression based on the range of $x$. The slope of the tangent is the derivative $\frac{dy}{dx}$ at the given point.Explanation:Given $x = -\frac{\pi}{4}$, which lies in the interval $[-\pi, 0]$. For $-\pi \le x \le 0$, the identity is $\cos^{-1}(\cos x) = -x$. Hence, $y = -x$.Differentiate with respect to $x$: $\frac{dy}{dx} = -1$.The derivative is constant, so the slope at $x = -\frac{\pi}{4}$ is also $-1$.Therefore, the slope of the tangent line is $-1$.Answer:-1 (Option A).