If `at a nalpha+bt a nbeta=(a+b)tan((alpha+beta)/2)` , where `alpha!=beta` , prove that `acosbeta=bcosalphadot`

Explanation

To prove that \( a \cos \beta = b \cos \alpha \) given the equation \( a \tan \alpha + b \tan \beta = (a + b) \tan\left(\frac{\alpha + \beta}{2}\right) \), we will follow these steps:

### Step 1: Start with the given equation
We have:
\[ a \tan \alpha + b \tan \beta = (a + b) \tan\left(\frac{\alpha + \beta}{2}\right) \]

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