Mathematics - Application of Derivative Question with Solution | TestHub

We know that $1\le |\sin x|+|\cos x|\le \sqrt{2};\therefore y=[|\sin x|+|\cos x|]=1$ The given curves meet at points where $y=1:x^2+1=5\Rightarrow x=\pm 2;\therefore P(2,1)$ and $Q(-2,1)$ Now $x^2+y^2=5\Rightarrow \frac{dy}{dx}=\frac{-x}{y},{\left(\frac{dy}{dx}\right)}_{(2,1)}=-2,{\left(\frac{dy}{dx}\right)}_{(-2,1)}=2$ Clearly the slope of line $y=1$ is 0 and the slope of tangent at P and Q are -2 and 2 respectively. $\therefore$ the angle of intersection is ${\tan }^{-1}(2)$