Oxford University MAT 2015 Solved Papers

I is false when $\mathit{x}=0$. II can be rearranged as ${\left(\sin \left(\mathit{x}\right)+1\right)}^2\ge \mathit{s}\mathit{l}\mathit{a}\mathit{n}\mathit{t}0$, using ${\cos }^2\left(\mathit{x}\right)+{\sin }^2\left(\mathit{x}\right)=1$, and hence is true. III translates the $\sin \left(\mathit{x}\right)$ graph by $\frac{3\mathit{\pi }}{2}$ along the $\mathit{x}$-axis, giving $\cos \left(\mathit{x}\right)$, and $\cos \left(\mathit{\pi }-\mathit{x}\right)$ translates the $\cos \left(\mathit{x}\right)$ graph by $\mathit{\pi }$ and reflects in the $\mathit{x}$-axis, giving $\cos \left(\mathit{x}\right)$, and hence is true. The answer is (c).