UPSKILL MATH PLUS

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Prove the following:
 
1. \((sin \ \alpha + cos \ \alpha)(tan \ \alpha + cot \ \alpha) = sec \ \alpha + cosec \ \alpha\)
 
2. \(1 + \frac{cot^2 \ \alpha}{1 + cosec \ \alpha} = cosec \ \alpha\)
 
Important!
This is a creative exercise. Your teacher will check it manually.