If `cos e ctheta-sintheta=m` and ` sectheta-costheta=n ,` prove that `(m^(2)n)^(2/3)+(m n^2)^(2/3)=1`

Explanation

To prove that \((m^2 n)^{2/3} + (mn^2)^{2/3} = 1\) given that \(m = \cos \theta - \sin \theta\) and \(n = \sec \theta - \cos \theta\), we will start by substituting the values of \(m\) and \(n\) into the left-hand side of the equation.

### Step-by-Step Solution:

1. **Substituting Values of m and n:**
\[ m = \cos \theta - \sin \theta, \quad n = \sec \theta - \cos \theta \]
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