What is the value of the following?

$\rm cosec\left(\dfrac{7\pi}{6}\right)sec\left(\dfrac{5\pi}{3}\right)$

If the determinant $\left| {\begin{array}{*{20}{c}} x&1&3\\ 0&0&1\\ 1&x&4 \end{array}} \right| = 0$ then what is x equal to?

What is the value of the following?

tan 31° tan 33° tan 35° _ _ _ _ _ tan 57° tan 59°

If 

$f(x)=\left|\begin{array}{ccc}1 & 1 & x+1 \\ 2 x & x(x-1) & x(x+1) \\ 3 x(x-1) & 2(x-1)(x-2) & x(x+1)(x-1)\end{array}\right|$ 

then what is f(-1) + f(0) + f(1) equal to?