Allied or Related Angles

If $A$ lies in the second quadrant and $3\tan A+4=0,$ then the value of $2\cot A-5\cos A+\sin A$ is equal to

Which of the following is correct?

If $\tan \theta =3$ and $\theta$ lies in third quadrant, then the value of $\sin \theta$ is 

The value of $\cos 1°·\cos 2°·\cos 3°·...·\cos 179°$is

If $x=\sec \theta -\tan \varphi \text{ and }y=cosec\varphi +\cot \varphi$ then show that $xy+x-y+1=0$.