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Simplify the following expressions completely: 1.1. sin πœƒ. cot πœƒ. sec πœƒ Answer: 1 1.2. sec πœƒ. cos πœƒ + π‘‘π‘Žπ‘›2πœƒ Answer: 𝑠𝑒𝑐2π‘₯ 1.3. sin π‘₯.sec π‘₯ Answer: tan π‘₯ 1.4. cos π‘₯ βˆ’ 1 Answer: βˆ’π‘ π‘–π‘›2π‘₯ sec π‘₯ 1.5. π‘π‘œπ‘‘2π‘₯(𝑠𝑒𝑐2π‘₯ βˆ’ 1) Answer: 1 1.6. 1 + 1 Answer: 2 tan π‘₯ sec π‘₯ cosec π‘₯βˆ’1 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. π‘π‘œπ‘ 2π‘₯ csc π‘₯ βˆ’ csc π‘₯ Answer: βˆ’ sin π‘₯ 1.12. π‘‘π‘Žπ‘›2π‘₯ βˆ’ π‘‘π‘Žπ‘›2π‘₯𝑠𝑖𝑛2π‘₯ Answer: 𝑠𝑖𝑛2π‘₯ 1.13. sin π‘₯ + cot π‘₯ cos π‘₯ Answer: csc π‘₯ 1.14. csc π‘₯ βˆ’ cos π‘₯π‘π‘œπ‘‘ 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: π‘π‘œπ‘‘2π‘₯ 𝑐𝑠𝑐 π‘₯ 𝑠𝑖𝑛2π‘₯π‘π‘œπ‘‘ π‘₯ 1.22. Answer: sin π‘₯ cos π‘₯ 1.23. 1π‘βˆ’π‘ π‘π‘ π‘–π‘›2βˆ’21π‘₯ Answer: π‘π‘œπ‘  π‘π‘œπ‘‘22π‘₯π‘₯ 1.24. π‘‘π‘Žπ‘›21π‘₯+1 Answer: π‘π‘œπ‘ 2π‘₯ 1.25. π‘‘π‘Žπ‘›2π‘₯ βˆ’ π‘‘π‘Žπ‘›2π‘₯ sin π‘₯ Answer: 𝑠𝑖𝑛2π‘₯ 1.26. 𝑠𝑖𝑛2π‘₯𝑐𝑠𝑐2π‘₯ βˆ’ 𝑠𝑖𝑛2π‘₯ Answer: π‘π‘œπ‘ 2π‘₯

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Answer to a math question Simplify the following expressions completely: 1.1. sin πœƒ. cot πœƒ. sec πœƒ Answer: 1 1.2. sec πœƒ. cos πœƒ + π‘‘π‘Žπ‘›2πœƒ Answer: 𝑠𝑒𝑐2π‘₯ 1.3. sin π‘₯.sec π‘₯ Answer: tan π‘₯ 1.4. cos π‘₯ βˆ’ 1 Answer: βˆ’π‘ π‘–π‘›2π‘₯ sec π‘₯ 1.5. π‘π‘œπ‘‘2π‘₯(𝑠𝑒𝑐2π‘₯ βˆ’ 1) Answer: 1 1.6. 1 + 1 Answer: 2 tan π‘₯ sec π‘₯ cosec π‘₯βˆ’1 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. π‘π‘œπ‘ 2π‘₯ csc π‘₯ βˆ’ csc π‘₯ Answer: βˆ’ sin π‘₯ 1.12. π‘‘π‘Žπ‘›2π‘₯ βˆ’ π‘‘π‘Žπ‘›2π‘₯𝑠𝑖𝑛2π‘₯ Answer: 𝑠𝑖𝑛2π‘₯ 1.13. sin π‘₯ + cot π‘₯ cos π‘₯ Answer: csc π‘₯ 1.14. csc π‘₯ βˆ’ cos π‘₯π‘π‘œπ‘‘ 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: π‘π‘œπ‘‘2π‘₯ 𝑐𝑠𝑐 π‘₯ 𝑠𝑖𝑛2π‘₯π‘π‘œπ‘‘ π‘₯ 1.22. Answer: sin π‘₯ cos π‘₯ 1.23. 1π‘βˆ’π‘ π‘π‘ π‘–π‘›2βˆ’21π‘₯ Answer: π‘π‘œπ‘  π‘π‘œπ‘‘22π‘₯π‘₯ 1.24. π‘‘π‘Žπ‘›21π‘₯+1 Answer: π‘π‘œπ‘ 2π‘₯ 1.25. π‘‘π‘Žπ‘›2π‘₯ βˆ’ π‘‘π‘Žπ‘›2π‘₯ sin π‘₯ Answer: 𝑠𝑖𝑛2π‘₯ 1.26. 𝑠𝑖𝑛2π‘₯𝑐𝑠𝑐2π‘₯ βˆ’ 𝑠𝑖𝑛2π‘₯ Answer: π‘π‘œπ‘ 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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