Using the principle of mathematical induction to prove that `int_(0)^(pi//2)(sin^2nx)/(sinx)dx=1+(1)/(3)+(1)/(5)+.....+(1)/(2n-1)`

Explanation

To prove the statement using the principle of mathematical induction, we will follow these steps:

**Step 1: Base Case (n = 1)**

We need to verify the statement for \( n = 1 \):
\[ \int_0^{\frac{\pi}{2}} \frac{\sin^2(1 \cdot x)}{\sin x} \, dx = 1 + \frac{1}{3} + \frac{1}{5} + \ldots + \frac{1}{2 \cdot 1 - 1} \]
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