Find the general solution of the trignometric equation `3^(1/2+log_(3)(cosx+sinx))-2^(log_(2)(cosx-sinx))=sqrt(2)`

Explanation

To solve the trigonometric equation \( 3^{\frac{1}{2} + \log_{3}(\cos x + \sin x)} - 2^{\log_{2}(\cos x - \sin x)} = \sqrt{2} \), we will follow these steps:

### Step 1: Simplify the equation
We start by rewriting the equation using properties of logarithms and exponents.

\[ 3^{\frac{1}{2}} \cdot 3^{\log_{3}(\cos x + \sin x)} - 2^{\log_{2}(\cos x - \sin x)} = \sqrt{2} \]
...