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2026-01-24 18:31:53
Giá trị của biểu thức A là 8/9
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2026-01-24 14:11:29
chào
2026-01-24 14:11:19
"Nắng cực" là một cách nói lóng, dân dã, dùng để diễn tả trạng thái nắng rất gắt, nắng to, nắng dữ dội (như nắng nóng kinh khủng), thường được dùng như một từ cảm thán để thể hiện sự khó chịu hoặc nhấn mạnh cường độ của ánh nắng mặt trời
2026-01-24 13:53:50
xin chào
2026-01-24 13:08:45
cs
2026-01-23 23:01:12
Bước 1: Tính các góc của tam giác ABCcap A cap B cap C𝐴𝐵𝐶 và các góc liên quan
OAsin∠OBA=ABsin∠AOB=ABsin(180∘−45∘−∠OBA)the fraction with numerator cap O cap A and denominator sine angle cap O cap B cap A end-fraction equals the fraction with numerator cap A cap B and denominator sine angle cap A cap O cap B end-fraction equals the fraction with numerator cap A cap B and denominator sine open paren 180 raised to the composed with power minus 45 raised to the composed with power minus angle cap O cap B cap A close paren end-fraction𝑂𝐴sin∠𝑂𝐵𝐴=𝐴𝐵sin∠𝐴𝑂𝐵=𝐴𝐵sin(180∘−45∘−∠𝑂𝐵𝐴) AB⋅sin75∘sin∠OBA=ABsin(135∘−∠OBA)the fraction with numerator cap A cap B center dot sine 75 raised to the composed with power and denominator sine angle cap O cap B cap A end-fraction equals the fraction with numerator cap A cap B and denominator sine open paren 135 raised to the composed with power minus angle cap O cap B cap A close paren end-fraction𝐴𝐵⋅sin75∘sin∠𝑂𝐵𝐴=𝐴𝐵sin(135∘−∠𝑂𝐵𝐴) sin75∘⋅sin(135∘−∠OBA)=sin∠OBAsine 75 raised to the composed with power center dot sine open paren 135 raised to the composed with power minus angle cap O cap B cap A close paren equals sine angle cap O cap B cap Asin75∘⋅sin(135∘−∠𝑂𝐵𝐴)=sin∠𝑂𝐵𝐴Khai triển phương trình lượng giác trên (với sin75∘=cos15∘sine 75 raised to the composed with power equals cosine 15 raised to the composed with powersin75∘=cos15∘):
cos15∘(sin135∘cos∠OBA−cos135∘sin∠OBA)=sin∠OBAcosine 15 raised to the composed with power open paren sine 135 raised to the composed with power cosine angle cap O cap B cap A minus cosine 135 raised to the composed with power sine angle cap O cap B cap A close paren equals sine angle cap O cap B cap Acos15∘(sin135∘cos∠𝑂𝐵𝐴−cos135∘sin∠𝑂𝐵𝐴)=sin∠𝑂𝐵𝐴 cos15∘(22cos∠OBA+22sin∠OBA)=sin∠OBAcosine 15 raised to the composed with power open paren the fraction with numerator the square root of 2 end-root and denominator 2 end-fraction cosine angle cap O cap B cap A plus the fraction with numerator the square root of 2 end-root and denominator 2 end-fraction sine angle cap O cap B cap A close paren equals sine angle cap O cap B cap Acos15∘(2√2cos∠𝑂𝐵𝐴+2√2sin∠𝑂𝐵𝐴)=sin∠𝑂𝐵𝐴 Chia cả hai vế cho cos∠OBAcosine angle cap O cap B cap Acos∠𝑂𝐵𝐴 và giải phương trình, ta tìm được:
tan∠OBA=1⇒∠OBA=45∘tangent angle cap O cap B cap A equals 1 implies angle cap O cap B cap A equals 45 raised to the composed with powertan∠𝑂𝐵𝐴=1⇒∠𝑂𝐵𝐴=45∘ Bước 4: Kết luận Trong △OABtriangle cap O cap A cap B△𝑂𝐴𝐵, ta có:
∠AOB=180∘−(∠OAB+∠OBA)=180∘−(45∘+45∘)=90∘angle cap A cap O cap B equals 180 raised to the composed with power minus open paren angle cap O cap A cap B plus angle cap O cap B cap A close paren equals 180 raised to the composed with power minus open paren 45 raised to the composed with power plus 45 raised to the composed with power close paren equals 90 raised to the composed with power∠𝐴𝑂𝐵=180∘−(∠𝑂𝐴𝐵+∠𝑂𝐵𝐴)=180∘−(45∘+45∘)=90∘ Đáp án: Vì ∠AOB=90∘angle cap A cap O cap B equals 90 raised to the composed with power∠𝐴𝑂𝐵=90∘, ta kết luận OA⟂OBcap O cap A ⟂ cap O cap B𝑂𝐴⟂𝑂𝐵. (đpcm)
- Trong △ABCtriangle cap A cap B cap C△𝐴𝐵𝐶, ta có:
∠C=180∘−(∠A+∠B)=180∘−(60∘+75∘)=45∘angle cap C equals 180 raised to the composed with power minus open paren angle cap A plus angle cap B close paren equals 180 raised to the composed with power minus open paren 60 raised to the composed with power plus 75 raised to the composed with power close paren equals 45 raised to the composed with power∠𝐶=180∘−(∠𝐴+∠𝐵)=180∘−(60∘+75∘)=45∘ - Theo giả thiết ∠OAC=15∘angle cap O cap A cap C equals 15 raised to the composed with power∠𝑂𝐴𝐶=15∘ và ∠OCB=15∘angle cap O cap C cap B equals 15 raised to the composed with power∠𝑂𝐶𝐵=15∘, ta tính được các góc kề:
- ∠OAB=∠A−∠OAC=60∘−15∘=45∘angle cap O cap A cap B equals angle cap A minus angle cap O cap A cap C equals 60 raised to the composed with power minus 15 raised to the composed with power equals 45 raised to the composed with power∠𝑂𝐴𝐵=∠𝐴−∠𝑂𝐴𝐶=60∘−15∘=45∘
- ∠OCA=∠C−∠OCB=45∘−15∘=30∘angle cap O cap C cap A equals angle cap C minus angle cap O cap C cap B equals 45 raised to the composed with power minus 15 raised to the composed with power equals 30 raised to the composed with power∠𝑂𝐶𝐴=∠𝐶−∠𝑂𝐶𝐵=45∘−15∘=30∘
- Trong △OACtriangle cap O cap A cap C△𝑂𝐴𝐶:
∠AOC=180∘−(∠OAC+∠OCA)=180∘−(15∘+30∘)=135∘angle cap A cap O cap C equals 180 raised to the composed with power minus open paren angle cap O cap A cap C plus angle cap O cap C cap A close paren equals 180 raised to the composed with power minus open paren 15 raised to the composed with power plus 30 raised to the composed with power close paren equals 135 raised to the composed with power∠𝐴𝑂𝐶=180∘−(∠𝑂𝐴𝐶+∠𝑂𝐶𝐴)=180∘−(15∘+30∘)=135∘
- Áp dụng định lý Sin trong △OACtriangle cap O cap A cap C△𝑂𝐴𝐶:
OAsin∠OCA=ACsin∠AOC⇒OA=AC⋅sin30∘sin135∘=AC⋅1222=AC2the fraction with numerator cap O cap A and denominator sine angle cap O cap C cap A end-fraction equals the fraction with numerator cap A cap C and denominator sine angle cap A cap O cap C end-fraction implies cap O cap A equals the fraction with numerator cap A cap C center dot sine 30 raised to the composed with power and denominator sine 135 raised to the composed with power end-fraction equals the fraction with numerator cap A cap C center dot one-half and denominator the fraction with numerator the square root of 2 end-root and denominator 2 end-fraction end-fraction equals the fraction with numerator cap A cap C and denominator the square root of 2 end-root end-fraction𝑂𝐴sin∠𝑂𝐶𝐴=𝐴𝐶sin∠𝐴𝑂𝐶⇒𝑂𝐴=𝐴𝐶⋅sin30∘sin135∘=𝐴𝐶⋅122√2=𝐴𝐶2√ - Áp dụng định lý Sin trong △ABCtriangle cap A cap B cap C△𝐴𝐵𝐶:
ACsin∠B=ABsin∠C⇒AC=AB⋅sin75∘sin45∘=AB⋅sin75∘22=2⋅AB⋅sin75∘the fraction with numerator cap A cap C and denominator sine angle cap B end-fraction equals the fraction with numerator cap A cap B and denominator sine angle cap C end-fraction implies cap A cap C equals the fraction with numerator cap A cap B center dot sine 75 raised to the composed with power and denominator sine 45 raised to the composed with power end-fraction equals the fraction with numerator cap A cap B center dot sine 75 raised to the composed with power and denominator the fraction with numerator the square root of 2 end-root and denominator 2 end-fraction end-fraction equals the square root of 2 end-root center dot cap A cap B center dot sine 75 raised to the composed with power𝐴𝐶sin∠𝐵=𝐴𝐵sin∠𝐶⇒𝐴𝐶=𝐴𝐵⋅sin75∘sin45∘=𝐴𝐵⋅sin75∘2√2=2√⋅𝐴𝐵⋅sin75∘ - Thay (2) vào (1), ta có độ dài OAcap O cap A𝑂𝐴:
OA=2⋅AB⋅sin75∘2=AB⋅sin75∘cap O cap A equals the fraction with numerator the square root of 2 end-root center dot cap A cap B center dot sine 75 raised to the composed with power and denominator the square root of 2 end-root end-fraction equals cap A cap B center dot sine 75 raised to the composed with power𝑂𝐴=2√⋅𝐴𝐵⋅sin75∘2√=𝐴𝐵⋅sin75∘ Bước 3: Tính góc ∠OBAangle cap O cap B cap A∠𝑂𝐵𝐴
OAsin∠OBA=ABsin∠AOB=ABsin(180∘−45∘−∠OBA)the fraction with numerator cap O cap A and denominator sine angle cap O cap B cap A end-fraction equals the fraction with numerator cap A cap B and denominator sine angle cap A cap O cap B end-fraction equals the fraction with numerator cap A cap B and denominator sine open paren 180 raised to the composed with power minus 45 raised to the composed with power minus angle cap O cap B cap A close paren end-fraction𝑂𝐴sin∠𝑂𝐵𝐴=𝐴𝐵sin∠𝐴𝑂𝐵=𝐴𝐵sin(180∘−45∘−∠𝑂𝐵𝐴) AB⋅sin75∘sin∠OBA=ABsin(135∘−∠OBA)the fraction with numerator cap A cap B center dot sine 75 raised to the composed with power and denominator sine angle cap O cap B cap A end-fraction equals the fraction with numerator cap A cap B and denominator sine open paren 135 raised to the composed with power minus angle cap O cap B cap A close paren end-fraction𝐴𝐵⋅sin75∘sin∠𝑂𝐵𝐴=𝐴𝐵sin(135∘−∠𝑂𝐵𝐴) sin75∘⋅sin(135∘−∠OBA)=sin∠OBAsine 75 raised to the composed with power center dot sine open paren 135 raised to the composed with power minus angle cap O cap B cap A close paren equals sine angle cap O cap B cap Asin75∘⋅sin(135∘−∠𝑂𝐵𝐴)=sin∠𝑂𝐵𝐴Khai triển phương trình lượng giác trên (với sin75∘=cos15∘sine 75 raised to the composed with power equals cosine 15 raised to the composed with powersin75∘=cos15∘):
cos15∘(sin135∘cos∠OBA−cos135∘sin∠OBA)=sin∠OBAcosine 15 raised to the composed with power open paren sine 135 raised to the composed with power cosine angle cap O cap B cap A minus cosine 135 raised to the composed with power sine angle cap O cap B cap A close paren equals sine angle cap O cap B cap Acos15∘(sin135∘cos∠𝑂𝐵𝐴−cos135∘sin∠𝑂𝐵𝐴)=sin∠𝑂𝐵𝐴 cos15∘(22cos∠OBA+22sin∠OBA)=sin∠OBAcosine 15 raised to the composed with power open paren the fraction with numerator the square root of 2 end-root and denominator 2 end-fraction cosine angle cap O cap B cap A plus the fraction with numerator the square root of 2 end-root and denominator 2 end-fraction sine angle cap O cap B cap A close paren equals sine angle cap O cap B cap Acos15∘(2√2cos∠𝑂𝐵𝐴+2√2sin∠𝑂𝐵𝐴)=sin∠𝑂𝐵𝐴 Chia cả hai vế cho cos∠OBAcosine angle cap O cap B cap Acos∠𝑂𝐵𝐴 và giải phương trình, ta tìm được:
tan∠OBA=1⇒∠OBA=45∘tangent angle cap O cap B cap A equals 1 implies angle cap O cap B cap A equals 45 raised to the composed with powertan∠𝑂𝐵𝐴=1⇒∠𝑂𝐵𝐴=45∘ Bước 4: Kết luận Trong △OABtriangle cap O cap A cap B△𝑂𝐴𝐵, ta có:
∠AOB=180∘−(∠OAB+∠OBA)=180∘−(45∘+45∘)=90∘angle cap A cap O cap B equals 180 raised to the composed with power minus open paren angle cap O cap A cap B plus angle cap O cap B cap A close paren equals 180 raised to the composed with power minus open paren 45 raised to the composed with power plus 45 raised to the composed with power close paren equals 90 raised to the composed with power∠𝐴𝑂𝐵=180∘−(∠𝑂𝐴𝐵+∠𝑂𝐵𝐴)=180∘−(45∘+45∘)=90∘ Đáp án: Vì ∠AOB=90∘angle cap A cap O cap B equals 90 raised to the composed with power∠𝐴𝑂𝐵=90∘, ta kết luận OA⟂OBcap O cap A ⟂ cap O cap B𝑂𝐴⟂𝑂𝐵. (đpcm)
2026-01-23 22:55:10
cs
2026-01-23 22:36:50
um
2026-01-23 22:34:42
chx
2025-11-22 17:40:35
hlo