Evaluate the following determinants: `|x-7x5x+1|` (ii) `|costheta-sinthetasinthetacostheta|` `|cos15^0sin15^0sin75^0cos75^0|` (iv) `|a+i b c+i d-c+i d a-i b|`

Explanation

Let's evaluate the given determinants step by step.

### (i) Determinant:
\[
\begin{vmatrix}
x & -7 \\
5x & 1
\end{vmatrix}
...