Which of the following function has period 2?

Which of the following can not be the direction cosines of a line?

If $A, B, C$ are $p^{\text {th }}, q^{\text {th }}$ and $r^{\text {th }}$ terms of a GP respectively then $A^{q-r} \cdot B^{r-p} \cdot C^{p-q}=\ldots \ldots$

$$\int_{\frac{\pi}{18}}^{\frac{4 \pi}{9}} \frac{2 \sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}} d x=\ldots \ldots$$