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1. Prove that \(\frac{sec \ \theta}{sin \ \theta} - \frac{sin \ \theta}{cos \ \theta} = cot \ \theta\)
2. Prove that \(sin^2 \ A \ cos^2 \ B + cos^2 \ A \ sin^2 \ B + cos^2 A \ cos^2 \ B + sin^2 \ A \ sin^2 \ B = 1\)
3. If \(cos \ \theta + sin \ \theta = \sqrt{2} \ cos \ \theta\), then prove that \(cos \ \theta - sin \ \theta = \sqrt{2} \ sin \ \theta\)
4. Prove that \((cosec \ \theta - sin \ \theta)(sec \ \theta - cos \ \theta)(tan \ \theta + cot \ \theta) = 1\)
5. Prove that \(\frac{sin \ A}{1 + cos \ A} + \frac{sin \ A}{1 - cos \ A} = 2 \ cosec \ A\)
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