Simplify each of the following: `cos^(-1)(3/5cosx+4/5sinx)` , where `-(3pi)/4lt=xlt=pi/4`

Explanation

To simplify the expression \( \cos^{-1}\left(\frac{3}{5}\cos x + \frac{4}{5}\sin x\right) \) where \( -\frac{3\pi}{4} < x < \frac{\pi}{4} \), we can follow these steps:

### Step 1: Recognize the coefficients
Notice that \( \frac{3}{5} \) and \( \frac{4}{5} \) can be interpreted as the cosine and sine of an angle \( \alpha \) in a right triangle.

### Step 2: Construct a right triangle
Construct a right triangle where:
- The adjacent side is \( 3 \)
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