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1. Prove that \(tan^2 \ \theta - sin^2 \ \theta = tan^2 \ \theta \ sin^2 \ \theta\)
2. Prove that \(\frac{sin \ A}{1 + cos \ A} = \frac{1 - cos \ A}{sin \ A}\)
3. Prove that \(1 + \frac{cot^2 \ \theta}{1 + cosec \ \theta} = cosec \ \theta\)
4. Prove that \(sec \ \theta - cos \ \theta = tan \ \theta \ sin \ \theta\)
5. Prove that \(\sqrt{\frac{1 + cos \ \theta}{1 - cos \ \theta}} = cosec \ \theta + cot \ \theta\)
Important!
This is a self-assessment task. Solve this question and assess the solution steps after completing the test on your own.
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