Question

The angle of intersection of curves y = [|sin x| + |cos x|] and x² + y² = 5 where [·] denotes the greatest integer function is

• A. tan^–1 (2)
• B. tan^–1$\left( \frac{1}{2} \right)$
• C. tan^–1$(\sqrt{2})$
• D. $\frac{\pi}{2}$

Answer 1

Answer: (A)

tan^–1 (2)

Answer 2

We know that 1 ≤ | sin x| + |cos x| ≤ $\sqrt{2}$

So that [|sin x| + |cos x|] will be constant function y = 1 No

Now intersection point P and Q are (–2, 1) and (2, 1)

Slope of line y = 1 is zero and slope of tangent at P and Q are (–2) and (2) respectively

Thus the angle of intersection is tan^–1 (2)