If `int \ sqrt(cos^3x/sin^11x) \ dx = -2(A tan^(9//2)x + B tan^(5//2) x) + C,` then find A and B.

Explanation

To solve the integral \( \int \sqrt{\frac{\cos^3 x}{\sin^{11} x}} \, dx \) and find the values of \( A \) and \( B \) from the expression \( -2(A \tan^{9/2} x + B \tan^{5/2} x) + C \), we will proceed step by step.

### Step 1: Rewrite the Integral
We start with the integral:
\[ I = \int \sqrt{\frac{\cos^3 x}{\sin^{11} x}} \, dx \]
This can be rewritten as:
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