Hitunglah a. cosec 30° tan 60° (sin 60°+cos 45°) b. sini 60° tan 30°+cosec 30° cotan 45° c. sini 30° + cos 60° + tan 60°/sec 60° cotan 30°

Jawabannya adalah a. cosec 30° tan 60° (sin 60°+cos 45°) = 3+ √6 b. sin 60° tan 30°+cosec 30° cotan 45° = 2½ c. sin 30° + cos 60° + tan 60°/sec 60° cotan 30° = 1½ Rumus cosec a = 1/ sin a cotan a = 1/tan a sec a = 1/cos a Sudut istimewa dalam identitas triginometri sin 30° = ½ sin 60° = ½√3 cos 45° = ½√2 cos 60° = ½ tan 30° = ⅓√3 tan 45° = 1 tan 60° = √3 Asumsikan soal Hitunglah a. cosec 30° tan 60° (sin 60°+cos 45°) b. sin 60° tan 30°+cosec 30° cotan 45° c. sin 30° + cos 60° + tan 60°/sec 60° cotan 30° a. cosec 30° tan 60° (sin 60°+cos 45°) =( 1/sin 30°) tan 60° (sin 60°+cos 45°) = (1/½)(√3)(½√3+½√2) = (2) (√3)(½)(√3+√2) = (√3)(√3+√2) = ((√3)(√3)) +((√2)(√3)) = 3 + √6 b. sin 60° tan 30°+cosec 30° cotan 45° =sin 60° tan 30°+(1/sin 30°) (1/tan 45°) = ((½√3)(⅓√3)) + (1/½)(1/1) = ((1/6) (3)) + 2(1) = ½ + 2 = 2½ c. sin 30° + cos 60° + tan 60°/sec 60° cotan 30° = sin 30° + cos 60° + tan 60°/((1/cos 60°)(1/tan 30°)) = ½ + ½ + √3 / ((1/½)(1/⅓√3)) = 1 + √3 / (2(3/√3)) = 1 + √3/ (6/√3) = 1 + √3 (√3/6) = 1 + 3/6 = 1 + ½ = 1½ Jadi jawabnya a. cosec 30° tan 60° (sin 60°+cos 45°) = 3+ √6 b. sin 60° tan 30°+cosec 30° cotan 45° = 2½ c. sin 30° + cos 60° + tan 60°/sec 60° cotan 30° = 1½