Let `0 lt A_(i) lt pi` for `i = 1,2,"……"n`. Use mathematical induction to prove that `sin A_(1) + sin A_(2)+ "….." + sin A_(n) le n sin ((A_(1) + A_(2) + "……" + A_(n))/(n))` where `n ge 1` is a natural number.
[You may use the fact that ` p sin x + (1-p) sin y le sin [px+(1-p)y]`, where `0 le p le 1` and `0 le x , y le pi`]

Explanation

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

### Step 1: Base Case
We need to check the base case for \( n = 1 \).

**Statement:**
For \( n = 1 \), we have:
\[
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