Question

Simplify the following expressions completely: 1.1. sin 𝜃. cot 𝜃. sec 𝜃 Answer: 1 1.2. sec 𝜃. cos 𝜃 + 𝑡𝑎𝑛2𝜃 Answer: 𝑠𝑒𝑐2𝑥 1.3. sin 𝑥.sec 𝑥 Answer: tan 𝑥 1.4. cos 𝑥 − 1 Answer: −𝑠𝑖𝑛2𝑥 sec 𝑥 1.5. 𝑐𝑜𝑡2𝑥(𝑠𝑒𝑐2𝑥 − 1) Answer: 1 1.6. 1 + 1 Answer: 2 tan 𝑥 sec 𝑥 cosec 𝑥−1 cosec 𝑥+1 1.7. sec 𝑥 cos 𝑥 Answer: 1 1.8. tan 𝑥 csc 𝑥 Answer: sec 𝑥 1.9. sec 𝑥 Answer: tan 𝑥 csc 𝑥 1.10. tan 𝑥 Answer: sin 𝑥 sec 𝑥 1.11. 𝑐𝑜𝑠2𝑥 csc 𝑥 − csc 𝑥 Answer: − sin 𝑥 1.12. 𝑡𝑎𝑛2𝑥 − 𝑡𝑎𝑛2𝑥𝑠𝑖𝑛2𝑥 Answer: 𝑠𝑖𝑛2𝑥 1.13. sin 𝑥 + cot 𝑥 cos 𝑥 Answer: csc 𝑥 1.14. csc 𝑥 − cos 𝑥𝑐𝑜𝑡 𝑥 Answer: sin 𝑥 1.15. tan 𝑥 csc 𝑥 Answer: tan 𝑥 1.16. cos 𝑥 tan 𝑥 Answer: sin 𝑥 1.17. cot 𝑥 sec 𝑥 Answer: csc 𝑥 1.18. (cos𝑥)(tan 𝑥)(csc 𝑥) Answer: 1 1.19. csc 𝑥 Answer: cot 𝑥 sec 𝑥 1.20. cot 𝑥 Answer: cos𝑥 tan 𝑥 1.21. cot 𝑥 Answer: 𝑐𝑜𝑡2𝑥 𝑐𝑠𝑐 𝑥 𝑠𝑖𝑛2𝑥𝑐𝑜𝑡 𝑥 1.22. Answer: sin 𝑥 cos 𝑥 1.23. 1𝑐−𝑠𝑐𝑠𝑖𝑛2−21𝑥 Answer: 𝑐𝑜𝑠 𝑐𝑜𝑡22𝑥𝑥 1.24. 𝑡𝑎𝑛21𝑥+1 Answer: 𝑐𝑜𝑠2𝑥 1.25. 𝑡𝑎𝑛2𝑥 − 𝑡𝑎𝑛2𝑥 sin 𝑥 Answer: 𝑠𝑖𝑛2𝑥 1.26. 𝑠𝑖𝑛2𝑥𝑐𝑠𝑐2𝑥 − 𝑠𝑖𝑛2𝑥 Answer: 𝑐𝑜𝑠2𝑥

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Answer to a math question Simplify the following expressions completely: 1.1. sin 𝜃. cot 𝜃. sec 𝜃 Answer: 1 1.2. sec 𝜃. cos 𝜃 + 𝑡𝑎𝑛2𝜃 Answer: 𝑠𝑒𝑐2𝑥 1.3. sin 𝑥.sec 𝑥 Answer: tan 𝑥 1.4. cos 𝑥 − 1 Answer: −𝑠𝑖𝑛2𝑥 sec 𝑥 1.5. 𝑐𝑜𝑡2𝑥(𝑠𝑒𝑐2𝑥 − 1) Answer: 1 1.6. 1 + 1 Answer: 2 tan 𝑥 sec 𝑥 cosec 𝑥−1 cosec 𝑥+1 1.7. sec 𝑥 cos 𝑥 Answer: 1 1.8. tan 𝑥 csc 𝑥 Answer: sec 𝑥 1.9. sec 𝑥 Answer: tan 𝑥 csc 𝑥 1.10. tan 𝑥 Answer: sin 𝑥 sec 𝑥 1.11. 𝑐𝑜𝑠2𝑥 csc 𝑥 − csc 𝑥 Answer: − sin 𝑥 1.12. 𝑡𝑎𝑛2𝑥 − 𝑡𝑎𝑛2𝑥𝑠𝑖𝑛2𝑥 Answer: 𝑠𝑖𝑛2𝑥 1.13. sin 𝑥 + cot 𝑥 cos 𝑥 Answer: csc 𝑥 1.14. csc 𝑥 − cos 𝑥𝑐𝑜𝑡 𝑥 Answer: sin 𝑥 1.15. tan 𝑥 csc 𝑥 Answer: tan 𝑥 1.16. cos 𝑥 tan 𝑥 Answer: sin 𝑥 1.17. cot 𝑥 sec 𝑥 Answer: csc 𝑥 1.18. (cos𝑥)(tan 𝑥)(csc 𝑥) Answer: 1 1.19. csc 𝑥 Answer: cot 𝑥 sec 𝑥 1.20. cot 𝑥 Answer: cos𝑥 tan 𝑥 1.21. cot 𝑥 Answer: 𝑐𝑜𝑡2𝑥 𝑐𝑠𝑐 𝑥 𝑠𝑖𝑛2𝑥𝑐𝑜𝑡 𝑥 1.22. Answer: sin 𝑥 cos 𝑥 1.23. 1𝑐−𝑠𝑐𝑠𝑖𝑛2−21𝑥 Answer: 𝑐𝑜𝑠 𝑐𝑜𝑡22𝑥𝑥 1.24. 𝑡𝑎𝑛21𝑥+1 Answer: 𝑐𝑜𝑠2𝑥 1.25. 𝑡𝑎𝑛2𝑥 − 𝑡𝑎𝑛2𝑥 sin 𝑥 Answer: 𝑠𝑖𝑛2𝑥 1.26. 𝑠𝑖𝑛2𝑥𝑐𝑠𝑐2𝑥 − 𝑠𝑖𝑛2𝑥 Answer: 𝑐𝑜𝑠2𝑥

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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)}}

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