Converting to Perfect Square

Q.

If S = $co{s}^2\frac{\pi }{n}+co{s}^2\frac{2\pi }{n}+........+co{s}^2\frac{(n-1)\pi }{n}$ then S is equal to

1. 

2. 

3. n/2

4. 

Q. If $f\left(x\right)=4x^4+12x^3+c{x}^2+6x+d$ is a perfect square, then

1. $c=5$
2. $c=13$
3. $d=1$
4. Minimum value of $f\left(x\right)$ occurs at $x=-\frac{1}{2}$