tolong dibantoo yaaaa flisss (tan 45 persen )²..... ketinggalan tadi pangkat 2
Matematika
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Pertanyaan
tolong dibantoo yaaaa flisss (tan 45 persen )²..... ketinggalan tadi pangkat 2
1 Jawaban
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1. Jawaban ErikCatosLawijaya
Mapel : Matematika
Kelas : X SMA
Bab : Trigonometri
Pembahasan :
Cos 45° / Sec 30° + Cosec 30°
= (1/2 √2) / [(2/3 √3) + 2]
= (3√2) / [(4√3 + 2)]
= (3√2)(4√3 - 2) / (4√3 + 2)(4√3 - 2)
= (12√6 - 6√2)/(48 - 4)
= (12√6 - 6√2)/44
= (6 - 3√2)/22
————————————————
[Sin 30° + Tan 45° - Cosec 60°]/[Sec 30° + Cos 60° + Cot 45°]
= [1/2 + 1 - 2/3√3]/[2/3 √3 + 1/2 + 1]
= [3/2 - 2/3√3]/[2/3√3 + 3/2]
= [9 - 4√3]/[4√3 + 9]
= (9 - 4√3)(4√3 - 9)/(4√3 + 9)(4√3 - 9)
= (72√3 - 129)/(48 - 81)
= (72√3 - 129)/-33
= (129 - 72√3)/33
————————————————
[2(Cos 60°)² + 4(Sec 30°)² - (Tan 45°)²]/[(Sin 30°)² + (Cos 30°)²]
= [2(1/2)² + 4(2/3 √3)² - (1)²]/[(1/2)² + (1/2√3)²]
= [2(1/4) + 4(12/9) - 1]/[1/4 + 3/4]
= [1/2 + 48/9 - 1]/1
= (9 + 96 - 18)/18
= 84/18
= 42/9