PUMPA - SMART LEARNING
எங்கள் ஆசிரியர்களுடன் 1-ஆன்-1 ஆலோசனை நேரத்தைப் பெறுங்கள். டாப்பர் ஆவதற்கு நாங்கள் பயிற்சி அளிப்போம்
Book Free Demo1. Prove the following identities.
(i) \(cot \ \theta + tan \ \theta = sec \ \theta \ cosec \ \theta\)
(ii) \(tan^4 \ \theta + tan^2 \ \theta = sec^4 \ \theta - sec^2 \ \theta\)
2. Prove the following identites.
(i) \(\frac{1 - tan^2 \ \theta}{cot^2 \ \theta - 1} = tan^2 \ \theta\)
(ii) \(\frac{cos \ \theta}{1 + sin \ \theta} = sec \ \theta - tan \ \theta\)
3. Prove the following identities.
(i) \(\sqrt{\frac{1 + sin \ \theta}{1 - sin \ \theta}} = sec \ \theta + tan \ \theta\)
(ii) \(\sqrt{\frac{1 + sin \ \theta}{1 - sin \ \theta}} + \sqrt{\frac{1 - sin \ \theta}{1 + sin \ \theta}} = 2 sec \ \theta\)
4. Prove the following identities.
(i) \(sec^6 \ \theta = tan^6 \ \theta + 3 tan^2 \ \theta \ sec^2 \ \theta + 1\)
(ii) \((sin \ \theta + sec \ \theta)^2 + (cos \ \theta + cosec \ \theta)^2 = 1 + (sec \ \theta + cosec \ \theta)^2\)
5. Prove the following identities.
(i) \(sec^4 \ \theta(1 - sin^4 \ \theta) - 2tan^2 \ \theta = 1\)
(ii) \(\frac{cot \ \theta - cos \ \theta}{cot \ \theta + cos \ \theta} = \frac{cosec \ \theta - 1}{cosec \ \theta + 1}\)
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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