31,37,43 \ II. Rewrite in terms of sine and cosine functions:the denominatoIn Problems 11-20, simplify each trigonometric expression by following the indicated direction.19. Factor and simplify: sin 0 + 2 sin e + 1SECTION 7.4 Trigonometric Identities 485Skill Buildinghe numerator andor by 1 + sing12. Rewrite in terms of sine and cosine functions:tan e. csc 0.cot 0 sec 0.cos 01- sin 01 + sin e-by1 + sin e\ 1L. Multiplysin 61 - cos 0by1- cos 0"14. Multiply15. Rewrite as a single quotient:sin 0 + cos 61 + cos 0cos e - sin 016. Rewrite as a single quotient:Cos esin 0= cos 6(sin e + cos 0) (sin e + cos 0) - 1cos v1 + cos v17. Multiply and simplify:(tan 0 + 1) (tan 0 + 1) - sec? 0sin e cos 018. Multiply and simplify:3 sin e + 4 sin e + 1tan 020. Factor and simplify:cos 0 - 1cos 0 - cos 0In Problems 21-100, establish each identity.\21. csc 0- cos 0 = cot 622. sec e. sin 0 = tan 023. 1 + tan? (-0) = sec? eestablish iden24. 1 + cot? (-0) = csc² 025. cos e (tan 0 + cot 0) = csc 026. sin 0 (cot 0 + tan 0) = sec 027. tan u cot u - cos u = sin? u28. sin u csc u - cos u = sin? u\ 29. (sec 0 - 1) (sec 0 + 1) = tan? 030. (csc 0 - 1) (csc 0 + 1) = cot? 031. (sec 0 + tan 6) (sec 0 - tan 0) = 1 32. (csc 0 + cot 0) (csc 0 - cot 0) = 133. cos? 0 (1 + tan? 0) = 134. (1 - cos 0) (1 + cot? 0) = 135. (sin 0 + cos 0)2 + (sin 0 - cos 0)2 = 2containing the m36. tan? 0 cos? 0 + cot? 0 sin? e = 137. sec* e - sec? 0 = tan 0 + tan? e38. csc* 0 - csc² 0 = cot 0 + cot? ecotient.cos usin u39. sec u - tan u40. csc u - cot u =41. 3 sin? 0 + 4 cos? 0 = 3 + cos 01 + sin u1 + cos und cosine funcioncos? 0sin? 01 - cos 042. 9 sec? 0 - 5 tan? 0 = 5 + 4 sec? 043. 1= sin 044. 1 -= - cos 01 + sin 0e of the expresinle.1 + tan v45.1cot v + 11 - sin vcsc v - 146.csc v +1sec e47.csc 0sin 6= 2 tan 0cos 0tan vcot v - 11+ sin vcsc e - 148.cot 01 + sin 049.1cos 0 + 150.cos 0 - 1cot ecsc 0 + 11 + seç 0%3Dcsc e + 1sin 6csc 0·11 - sec 01 - sin v51.CoS V1 + sin vsin 0cos v1= 2 sec v52.= 2 sec v53.sin 0 - cos 6%3Dcos v1- sin vsin vcos V1- cot 0listed in rad1 - cos 056.1 + cos 0sin? 0sin o54. 1= cos 0= (sec 0 - tan 0)2(csc 0 – cot 0)21 + cos e1+sin 9Os 0- sine pcot 0tan 0cos 057.1- tan 0sin 0sin 0 + cos58.1= 1 + tan 0 + cot 0cot 01 - cot 0tan 01tan 0 + sec 0 - 161.tan 0 - sec 0 + 1cos esin 0 cos 0tan 0= tan 0 + sec 059. tan 0 +1 + sin 0= sec 060.cos 0 – sin? 01- tan? 0sin 0sin 0 - cos 0 + 162,sin 0 + cos 0 - 1tan 0 - cot 063.tan 0 + cot 0sec 0 - cos 064.sec 0 + cos 0sin 0 + 1= sin? 0 – cos² equations i1 + cos? 0cos 0tan u - cot u66.tan u + cot usec 0 + tan 067.cot 0 + cos 0tan u - cot u+ 2 cos? u = 1= tan 0 sec 065.tan u + cot u+ 1 = 2 sin? u1 – tan² 069.1 + tan? 61 - cot? 070.1 + cot? 0sind1 - cos 0+ 2 cos? 0 = 1seç 0+ 1 = 2 cos? 068.1+ sec 0sin? 0sin? 0 – tan 072.cos? 0 - cot 071 sec 0 – csc 0tan? 073. sec 0 - cos 0 = sin 0 tan 071.sec 0 csc 0= sin 0 - cos 01 + sin 076.1 - sin 01 - sin 01 + sin 01= 2 seç? 0= 4 tan 0 sec 074. tan 0 + cot 0 = sec 0 csc 075.sin 01 + sin 0denominatoR

Question

31,37,43 \ II. Rewrite in terms of sine and cosine functions:the denominatoIn Problems 11-20, simplify each trigonometric expression by following the indicated direction.19. Factor and simplify: sin 0 + 2 sin e + 1SECTION 7.4 Trigonometric Identities 485Skill Buildinghe numerator andor by 1 + sing12. Rewrite in terms of sine and cosine functions:tan e. csc 0.cot 0 sec 0.cos 01- sin 01 + sin e-by1 + sin e\ 1L. Multiplysin 61 - cos 0by1- cos 0&#34;14. Multiply15. Rewrite as a single quotient:sin 0 + cos 61 + cos 0cos e - sin 016. Rewrite as a single quotient:Cos esin 0= cos 6(sin e + cos 0) (sin e + cos 0) - 1cos v1 + cos v17. Multiply and simplify:(tan 0 + 1) (tan 0 + 1) - sec? 0sin e cos 018. Multiply and simplify:3 sin e + 4 sin e + 1tan 020. Factor and simplify:cos 0 - 1cos 0 - cos 0In Problems 21-100, establish each identity.\21. csc 0- cos 0 = cot 622. sec e. sin 0 = tan 023. 1 + tan? (-0) = sec? eestablish iden24. 1 + cot? (-0) = csc² 025. cos e (tan 0 + cot 0) = csc 026. sin 0 (cot 0 + tan 0) = sec 027. tan u cot u - cos u = sin? u28. sin u csc u - cos u = sin? u\ 29. (sec 0 - 1) (sec 0 + 1) = tan? 030. (csc 0 - 1) (csc 0 + 1) = cot? 031. (sec 0 + tan 6) (sec 0 - tan 0) = 1 32. (csc 0 + cot 0) (csc 0 - cot 0) = 133. cos? 0 (1 + tan? 0) = 134. (1 - cos 0) (1 + cot? 0) = 135. (sin 0 + cos 0)2 + (sin 0 - cos 0)2 = 2containing the m36. tan? 0 cos? 0 + cot? 0 sin? e = 137. sec* e - sec? 0 = tan 0 + tan? e38. csc* 0 - csc² 0 = cot 0 + cot? ecotient.cos usin u39. sec u - tan u40. csc u - cot u =41. 3 sin? 0 + 4 cos? 0 = 3 + cos 01 + sin u1 + cos und cosine funcioncos? 0sin? 01 - cos 042. 9 sec? 0 - 5 tan? 0 = 5 + 4 sec? 043. 1= sin 044. 1 -= - cos 01 + sin 0e of the expresinle.1 + tan v45.1cot v + 11 - sin vcsc v - 146.csc v +1sec e47.csc 0sin 6= 2 tan 0cos 0tan vcot v - 11+ sin vcsc e - 148.cot 01 + sin 049.1cos 0 + 150.cos 0 - 1cot ecsc 0 + 11 + seç 0%3Dcsc e + 1sin 6csc 0·11 - sec 01 - sin v51.CoS V1 + sin vsin 0cos v1= 2 sec v52.= 2 sec v53.sin 0 - cos 6%3Dcos v1- sin vsin vcos V1- cot 0listed in rad1 - cos 056.1 + cos 0sin? 0sin o54. 1= cos 0= (sec 0 - tan 0)2(csc 0 – cot 0)21 + cos e1+sin 9Os 0- sine pcot 0tan 0cos 057.1- tan 0sin 0sin 0 + cos58.1= 1 + tan 0 + cot 0cot 01 - cot 0tan 01tan 0 + sec 0 - 161.tan 0 - sec 0 + 1cos esin 0 cos 0tan 0= tan 0 + sec 059. tan 0 +1 + sin 0= sec 060.cos 0 – sin? 01- tan? 0sin 0sin 0 - cos 0 + 162,sin 0 + cos 0 - 1tan 0 - cot 063.tan 0 + cot 0sec 0 - cos 064.sec 0 + cos 0sin 0 + 1= sin? 0 – cos² equations i1 + cos? 0cos 0tan u - cot u66.tan u + cot usec 0 + tan 067.cot 0 + cos 0tan u - cot u+ 2 cos? u = 1= tan 0 sec 065.tan u + cot u+ 1 = 2 sin? u1 – tan² 069.1 + tan? 61 - cot? 070.1 + cot? 0sind1 - cos 0+ 2 cos? 0 = 1seç 0+ 1 = 2 cos? 068.1+ sec 0sin? 0sin? 0 – tan 072.cos? 0 - cot 071 sec 0 – csc 0tan? 073. sec 0 - cos 0 = sin 0 tan 071.sec 0 csc 0= sin 0 - cos 01 + sin 076.1 - sin 01 - sin 01 + sin 01= 2 seç? 0= 4 tan 0 sec 074. tan 0 + cot 0 = sec 0 csc 075.sin 01 + sin 0denominatoR

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