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(sinalpha + cosalpha)(tanalpha + cotalph...

`(sinalpha + cosalpha)(tanalpha + cotalpha) = secalpha + cosecalpha`

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To prove the equation \((\sin \alpha + \cos \alpha)(\tan \alpha + \cot \alpha) = \sec \alpha + \csc \alpha\), we will start with the left-hand side (LHS) and manipulate it to show that it equals the right-hand side (RHS). ### Step-by-Step Solution: 1. **Start with the Left-Hand Side (LHS)**: \[ \text{LHS} = (\sin \alpha + \cos \alpha)(\tan \alpha + \cot \alpha) \] ...
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