If ∫ sec x cosec x dx = log |g(x)| + c, then what is g(x) equal to?

• A. sin x cos x
• B. sec² x
• C. tan x
• D. log |tan x|

To solve the integral ∫ sec x cosec x dx, we can simplify the expression. The integrand sec x cosec x can be rewritten as:

• sec x = 1/cos x
• cosec x = 1/sin x

Thus, sec x cosec x becomes:

sec x cosec x = 1/(sin x cos x)

Integrating this gives us:

∫ sec x cosec x dx = ∫ (1/(sin x cos x)) dx = ∫ (2/(sin(2x))) dx

This integral leads to a logarithmic function, specifically:

log |g(x)| + c

From the options provided, we need to identify which function corresponds to the integral. The correct choice is:

g(x) = sin x cos x

Therefore, the answer is:

A. sin x cos x