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

Explanation

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

### Step 1: Identify the components
We recognize that the coefficients \( \frac{3}{5} \) and \( \frac{4}{5} \) can be related to the sides of a right triangle. Specifically, they correspond to the adjacent and opposite sides of a triangle with a hypotenuse of 5.

### Step 2: Define the angle
Let \( \alpha \) be an angle such that:
- \( \cos \alpha = \frac{3}{5} \)
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