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Simplify the following expressions completely: 1.1. sin ๐œƒ. cot ๐œƒ. sec ๐œƒ Answer: 1 1.2. sec ๐œƒ. cos ๐œƒ + ๐‘ก๐‘Ž๐‘›2๐œƒ Answer: ๐‘ ๐‘’๐‘2๐‘ฅ 1.3. sin ๐‘ฅ.sec ๐‘ฅ Answer: tan ๐‘ฅ 1.4. cos ๐‘ฅ โˆ’ 1 Answer: โˆ’๐‘ ๐‘–๐‘›2๐‘ฅ sec ๐‘ฅ 1.5. ๐‘๐‘œ๐‘ก2๐‘ฅ(๐‘ ๐‘’๐‘2๐‘ฅ โˆ’ 1) Answer: 1 1.6. 1 + 1 Answer: 2 tan ๐‘ฅ sec ๐‘ฅ cosec ๐‘ฅโˆ’1 cosec ๐‘ฅ+1 1.7. sec ๐‘ฅ cos ๐‘ฅ Answer: 1 1.8. tan ๐‘ฅ csc ๐‘ฅ Answer: sec ๐‘ฅ 1.9. sec ๐‘ฅ Answer: tan ๐‘ฅ csc ๐‘ฅ 1.10. tan ๐‘ฅ Answer: sin ๐‘ฅ sec ๐‘ฅ 1.11. ๐‘๐‘œ๐‘ 2๐‘ฅ csc ๐‘ฅ โˆ’ csc ๐‘ฅ Answer: โˆ’ sin ๐‘ฅ 1.12. ๐‘ก๐‘Ž๐‘›2๐‘ฅ โˆ’ ๐‘ก๐‘Ž๐‘›2๐‘ฅ๐‘ ๐‘–๐‘›2๐‘ฅ Answer: ๐‘ ๐‘–๐‘›2๐‘ฅ 1.13. sin ๐‘ฅ + cot ๐‘ฅ cos ๐‘ฅ Answer: csc ๐‘ฅ 1.14. csc ๐‘ฅ โˆ’ cos ๐‘ฅ๐‘๐‘œ๐‘ก ๐‘ฅ Answer: sin ๐‘ฅ 1.15. tan ๐‘ฅ csc ๐‘ฅ Answer: tan ๐‘ฅ 1.16. cos ๐‘ฅ tan ๐‘ฅ Answer: sin ๐‘ฅ 1.17. cot ๐‘ฅ sec ๐‘ฅ Answer: csc ๐‘ฅ 1.18. (cos๐‘ฅ)(tan ๐‘ฅ)(csc ๐‘ฅ) Answer: 1 1.19. csc ๐‘ฅ Answer: cot ๐‘ฅ sec ๐‘ฅ 1.20. cot ๐‘ฅ Answer: cos๐‘ฅ tan ๐‘ฅ 1.21. cot ๐‘ฅ Answer: ๐‘๐‘œ๐‘ก2๐‘ฅ ๐‘๐‘ ๐‘ ๐‘ฅ ๐‘ ๐‘–๐‘›2๐‘ฅ๐‘๐‘œ๐‘ก ๐‘ฅ 1.22. Answer: sin ๐‘ฅ cos ๐‘ฅ 1.23. 1๐‘โˆ’๐‘ ๐‘๐‘ ๐‘–๐‘›2โˆ’21๐‘ฅ Answer: ๐‘๐‘œ๐‘  ๐‘๐‘œ๐‘ก22๐‘ฅ๐‘ฅ 1.24. ๐‘ก๐‘Ž๐‘›21๐‘ฅ+1 Answer: ๐‘๐‘œ๐‘ 2๐‘ฅ 1.25. ๐‘ก๐‘Ž๐‘›2๐‘ฅ โˆ’ ๐‘ก๐‘Ž๐‘›2๐‘ฅ sin ๐‘ฅ Answer: ๐‘ ๐‘–๐‘›2๐‘ฅ 1.26. ๐‘ ๐‘–๐‘›2๐‘ฅ๐‘๐‘ ๐‘2๐‘ฅ โˆ’ ๐‘ ๐‘–๐‘›2๐‘ฅ Answer: ๐‘๐‘œ๐‘ 2๐‘ฅ

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Answer to a math question Simplify the following expressions completely: 1.1. sin ๐œƒ. cot ๐œƒ. sec ๐œƒ Answer: 1 1.2. sec ๐œƒ. cos ๐œƒ + ๐‘ก๐‘Ž๐‘›2๐œƒ Answer: ๐‘ ๐‘’๐‘2๐‘ฅ 1.3. sin ๐‘ฅ.sec ๐‘ฅ Answer: tan ๐‘ฅ 1.4. cos ๐‘ฅ โˆ’ 1 Answer: โˆ’๐‘ ๐‘–๐‘›2๐‘ฅ sec ๐‘ฅ 1.5. ๐‘๐‘œ๐‘ก2๐‘ฅ(๐‘ ๐‘’๐‘2๐‘ฅ โˆ’ 1) Answer: 1 1.6. 1 + 1 Answer: 2 tan ๐‘ฅ sec ๐‘ฅ cosec ๐‘ฅโˆ’1 cosec ๐‘ฅ+1 1.7. sec ๐‘ฅ cos ๐‘ฅ Answer: 1 1.8. tan ๐‘ฅ csc ๐‘ฅ Answer: sec ๐‘ฅ 1.9. sec ๐‘ฅ Answer: tan ๐‘ฅ csc ๐‘ฅ 1.10. tan ๐‘ฅ Answer: sin ๐‘ฅ sec ๐‘ฅ 1.11. ๐‘๐‘œ๐‘ 2๐‘ฅ csc ๐‘ฅ โˆ’ csc ๐‘ฅ Answer: โˆ’ sin ๐‘ฅ 1.12. ๐‘ก๐‘Ž๐‘›2๐‘ฅ โˆ’ ๐‘ก๐‘Ž๐‘›2๐‘ฅ๐‘ ๐‘–๐‘›2๐‘ฅ Answer: ๐‘ ๐‘–๐‘›2๐‘ฅ 1.13. sin ๐‘ฅ + cot ๐‘ฅ cos ๐‘ฅ Answer: csc ๐‘ฅ 1.14. csc ๐‘ฅ โˆ’ cos ๐‘ฅ๐‘๐‘œ๐‘ก ๐‘ฅ Answer: sin ๐‘ฅ 1.15. tan ๐‘ฅ csc ๐‘ฅ Answer: tan ๐‘ฅ 1.16. cos ๐‘ฅ tan ๐‘ฅ Answer: sin ๐‘ฅ 1.17. cot ๐‘ฅ sec ๐‘ฅ Answer: csc ๐‘ฅ 1.18. (cos๐‘ฅ)(tan ๐‘ฅ)(csc ๐‘ฅ) Answer: 1 1.19. csc ๐‘ฅ Answer: cot ๐‘ฅ sec ๐‘ฅ 1.20. cot ๐‘ฅ Answer: cos๐‘ฅ tan ๐‘ฅ 1.21. cot ๐‘ฅ Answer: ๐‘๐‘œ๐‘ก2๐‘ฅ ๐‘๐‘ ๐‘ ๐‘ฅ ๐‘ ๐‘–๐‘›2๐‘ฅ๐‘๐‘œ๐‘ก ๐‘ฅ 1.22. Answer: sin ๐‘ฅ cos ๐‘ฅ 1.23. 1๐‘โˆ’๐‘ ๐‘๐‘ ๐‘–๐‘›2โˆ’21๐‘ฅ Answer: ๐‘๐‘œ๐‘  ๐‘๐‘œ๐‘ก22๐‘ฅ๐‘ฅ 1.24. ๐‘ก๐‘Ž๐‘›21๐‘ฅ+1 Answer: ๐‘๐‘œ๐‘ 2๐‘ฅ 1.25. ๐‘ก๐‘Ž๐‘›2๐‘ฅ โˆ’ ๐‘ก๐‘Ž๐‘›2๐‘ฅ sin ๐‘ฅ Answer: ๐‘ ๐‘–๐‘›2๐‘ฅ 1.26. ๐‘ ๐‘–๐‘›2๐‘ฅ๐‘๐‘ ๐‘2๐‘ฅ โˆ’ ๐‘ ๐‘–๐‘›2๐‘ฅ Answer: ๐‘๐‘œ๐‘ 2๐‘ฅ

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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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