Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

Let $f(x)=\sin (\cos x)+\cos (\sin x);f$ is even and decreasing on $\left[0,\frac{\pi }{2}\right]$, so its maximum is $f(0)=\sin 1+1$ (a-s) and its minimum is $f\left(\frac{\pi }{2}\right)=\cos 1$ (b-r). Let $g(x)=\cos (\cos (\sin x));g$ is even, periodic with period $\pi$, and increasing on $\left[0,\frac{\pi }{2}\right]$, so its maximum is $g\left(\frac{\pi }{2}\right)=\cos (\cos 1)$ (c-p) and its minimum is $g(0)=\cos 1$ (d-r).