Question

Simplify the following expressions completely: 1.1. sin π. cot π. sec π Answer: 1 1.2. sec π. cos π + π‘ππ2π Answer: π ππ2π₯ 1.3. sin π₯.sec π₯ Answer: tan π₯ 1.4. cos π₯ β 1 Answer: βπ ππ2π₯ sec π₯ 1.5. πππ‘2π₯(π ππ2π₯ β 1) Answer: 1 1.6. 1 + 1 Answer: 2 tan π₯ sec π₯ cosec π₯β1 cosec π₯+1 1.7. sec π₯ cos π₯ Answer: 1 1.8. tan π₯ csc π₯ Answer: sec π₯ 1.9. sec π₯ Answer: tan π₯ csc π₯ 1.10. tan π₯ Answer: sin π₯ sec π₯ 1.11. πππ 2π₯ csc π₯ β csc π₯ Answer: β sin π₯ 1.12. π‘ππ2π₯ β π‘ππ2π₯π ππ2π₯ Answer: π ππ2π₯ 1.13. sin π₯ + cot π₯ cos π₯ Answer: csc π₯ 1.14. csc π₯ β cos π₯πππ‘ π₯ Answer: sin π₯ 1.15. tan π₯ csc π₯ Answer: tan π₯ 1.16. cos π₯ tan π₯ Answer: sin π₯ 1.17. cot π₯ sec π₯ Answer: csc π₯ 1.18. (cosπ₯)(tan π₯)(csc π₯) Answer: 1 1.19. csc π₯ Answer: cot π₯ sec π₯ 1.20. cot π₯ Answer: cosπ₯ tan π₯ 1.21. cot π₯ Answer: πππ‘2π₯ ππ π π₯ π ππ2π₯πππ‘ π₯ 1.22. Answer: sin π₯ cos π₯ 1.23. 1πβπ ππ ππ2β21π₯ Answer: πππ πππ‘22π₯π₯ 1.24. π‘ππ21π₯+1 Answer: πππ 2π₯ 1.25. π‘ππ2π₯ β π‘ππ2π₯ sin π₯ Answer: π ππ2π₯ 1.26. π ππ2π₯ππ π2π₯ β π ππ2π₯ Answer: πππ 2π₯

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for question 1
\sin{(\theta)}.\cot{(\theta)}.\sec{(\theta)}
=\sin{(\theta)}.\frac{1}{\tan{(\theta)}}.\frac{1}{\cos{(\theta)}}
=\sin{(\theta)}.\frac{\cos{(\theta)}}{\sin{(\theta)}}.\frac{1}{\cos{(\theta)}}
=1

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