Prove that `I_(1),I_(2),I_(3)"..."` form an AP, if
`I_(n)=int_(0)^(pi)(sin2nx)/(sinx)dx` .

Explanation

To prove that \( I_1, I_2, I_3, \ldots \) form an arithmetic progression (AP), we start by defining the integral:

\[ I_n = \int_0^{\pi} \frac{\sin(2nx)}{\sin(x)} \, dx \]

### Step 1: Understanding the Integral
We have \( I_n \) defined as the integral of \( \frac{\sin(2nx)}{\sin(x)} \) from \( 0 \) to \( \pi \).
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