Question

If \[ \int\frac1{1+\cos x}\,dx = \frac1{f\!\left(\frac x2\right)}+C_1, \] then \[ \int f(x)\,dx= \ ? \]

• A. \(\log|\sin x|+C\)
• B. \(\log|\cos x|+C\)
• C. \(-\csc^2x+C\)
• D. \(\tan x+C\)

Hint:

Remember: \[ \int \cot x\,dx=\log|\sin x|+C. \] and \[ \int \tan x\,dx=-\log|\cos x|+C. \]

Answer 1

The Correct Option is A