Sum of Sines of Angles in Arithmetic Progression

Q. The average value of $\sin 2°,\sin 4°,\sin 6°,...,\sin 180°\mathrm{is}$

1. 
   $\frac{1}{90}\cot 1°$
2. 
   $\frac{1}{90}\tan 1°$
3. 
   $\frac{1}{90}\tan 89°$
4. 
   $\frac{1}{90}\cot 89°$

Q. The average of $m\sin \left(m^{\circ }\right)$ where $m=2,4,6,\cdots ,180$ is equal to
(correct answer + 1, wrong answer - 0.25)

1. $\cot {89}^{\circ }$
2. $\cot 1^{\circ }$
3. $\tan 1^{\circ }$
4. $90\sin {89}^{\circ }$

Q. If $\sin \frac{\pi }{14}\sin \frac{3\pi }{14}\sin \frac{5\pi }{14}\sin \frac{7\pi }{14}\sin \frac{9\pi }{14}\sin \frac{11\pi }{14}\sin \frac{13\pi }{14}=\frac{1}{k},$ then $k$ is equal to

Q. The average of $m\sin \left(m^{\circ }\right)$ where $m=2,4,6,\cdots ,180$ is equal to
(correct answer + 1, wrong answer - 0.25)

1. $\cot {89}^{\circ }$
2. $\cot 1^{\circ }$
3. $\tan 1^{\circ }$
4. $90\sin {89}^{\circ }$

Q.

If $S=\sin \frac{\pi }{n}+\sin \frac{3\pi }{n}+\sin \frac{5\pi }{n}+\cdot \cdot \cdot n$ terms.
Then the value $nS$ is

Q. The average value of $\sin 2°,\sin 4°,\sin 6°,...,\sin 180°\mathrm{is}$

1. 
   $\frac{1}{90}\cot 1°$
2. 
   $\frac{1}{90}\tan 1°$
3. 
   $\frac{1}{90}\tan 89°$
4. 
   $\frac{1}{90}\cot 89°$

Q. If $\sin \frac{\pi }{14}\sin \frac{3\pi }{14}\sin \frac{5\pi }{14}\sin \frac{7\pi }{14}\sin \frac{9\pi }{14}\sin \frac{11\pi }{14}\sin \frac{13\pi }{14}=\frac{1}{k},$ then $k$ is equal to