If $\theta$ is the angle of intersection of curves $y = [|\sin x| + |\cos x|]$ and $x^2 + y^2 = 5$. Then the value of $|\tan \theta|$ is ________. (where $[.]$ denotes G.I.F.)
Step-by-Step Solution
Key Concept: Find intersection points explicitly, then use implicit differentiation to compute slopes at those points.
The constraint is $|\sin x| + |\cos x| = \sqrt{2}$, which simplifies to $y = |\sin x| + |\cos x| = 1$. The intersection points of the curve $x^2 + y^2 = 5$ with this constraint are $(2,1)$ and $(-2,1)$. Using implicit differentiation: $2x + 2y dy/dx = 0$, so $dy/dx = -x/y$. At $(2,1)$: $dy/dx = -2$, and at $(-2,1)$: $dy/dx = 2$.
Correct Answer: 2