Match the pairs correctly:
(i) \( \int \tan x \, dx \) \(\hspace{3.5cm}\) \( \log |\sin x| + c \)
(ii) \( \int \cot x \, dx \) \(\hspace{3.5cm}\) \( \log |\csc x| - \cot x + c \)
(iii) \( \int \sec x \, dx \) \(\hspace{3.5cm}\) \( \log |\sec x + \tan x| + c \)
(iv) \( \int \csc x \, dx \) \(\hspace{3.5cm}\) \( -\log |\csc x + \cot x| + c \)
(v) \( \int \frac{\cos x}{\sin x} \, dx \) \(\hspace{3.5cm}\) \( \log |\sin x| + c \)
(vi) Derivative of \( \sin 2x \) with respect to \( x \) \(\hspace{0.75cm}\) \( 2 \cos 2x \)