If `x ne (npi)/2, n in I` and `(cosx)^(sin^(2)x-3sinx+2)=1`, then find the general solutions of x.

Explanation

To solve the equation \((\cos x)^{(\sin^2 x - 3\sin x + 2)} = 1\) under the condition that \(x \neq \frac{n\pi}{2}\) where \(n\) is an integer, we can follow these steps:

### Step 1: Rewrite the Equation
We know that any number raised to the power of 0 is equal to 1. Therefore, we can set the exponent equal to 0:
\[ \sin^2 x - 3\sin x + 2 = 0 \]

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