Question : If $\sec \theta+\tan \theta=\frac{1}{\sqrt{3}}$, then the positive value of $\cot \theta+\cos \theta$ is:

Question : If $\theta$ is an acute angle and $\sin \theta \cos \theta=2 \cos ^3 \theta-\frac{1}{4} \cos \theta$, then the value of $\sin \theta$ is:

Question : If $\sqrt{2} \sec ^2 \theta-4 \sec \theta+2 \sqrt{2}=0$, then what is the value $\sin ^2 \theta+\tan ^2 \theta$?

Question : If $\cos \theta+\sin \theta=\sqrt{2}$, then what is the value of $\sec \theta \operatorname{cosec} \theta$ ?

Question : If $(r\cos \theta -\sqrt{3})^{2}+(r\sin \theta -1)^{2}=0$, then the value of $\frac{r\tan \theta +\sec \theta}{r\sec \theta +\tan\theta}$ is equal to: