Evaluate: ∫ log tan x .dx, x ∈ [0,π​​​​​​​/2]

Question

Evaluate:

\(\int_0^{\pi/2}\) log tan \(x\) ⋅ \(dx\)

∫ log tan x .dx, x ∈ [0,π/2]

Answer 1

Let \(I = \) \(\int_0^{\pi/2}\) log tan \(x\) ⋅ \(dx\)

We use the property,

Here, a = \(\pi/2\). Here changing x by \(\pi/2\) - x, We get