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Trigonometry # Exam ✅

If tan 10 = x then

Figure it out. Use tan (A-B) to solve this problem. Practice it.

# ExamIn case you meet in school 🥳

2025/7/7 Edited to

ข้อนี้เป็นโจทย์ที่ชอบออกแนว “จัดรูปให้เป็นสูตร tan(A±B)” ก่อน แล้วค่อยแทนค่าจาก tan 10° = x ค่ะ จุดสำคัญคืออย่าเพิ่งรีบกระจาย ให้สังเกตรูปของเศษส่วนก่อน 1) จำสูตรให้แม่น (ใช้บ่อยมากในข้อสอบ) - tan(A−B) = (tanA − tanB) / (1 + tanA tanB) - tan(A+B) = (tanA + tanB) / (1 − tanA tanB) โจทย์นี้ให้มาเป็น (tan188° − tan108°) / (1 + tan188°tan108°) ซึ่ง “ตรงเป๊ะ” กับ tan(A−B) ทันที 2) จับคู่มุมให้เป็น A−B ให้ A = 188° และ B = 108° ดังนั้น นิพจน์ทั้งหมด = tan(188°−108°) = tan 80° แค่นี้โจทย์ก็เหลือแค่หาค่า tan80° จาก tan10° = x 3) แปลง tan80° ให้โยงกับ tan10° ใช้ความสัมพันธ์มุมเติมเต็ม (co-function): tan(90°−θ) = cot θ = 1/tanθ เพราะ 80° = 90° − 10° ดังนั้น tan80° = tan(90°−10°) = cot10° = 1/tan10° 4) แทนค่าตามกำหนด เมื่อ tan10° = x ⇒ tan80° = 1/x สรุปคำตอบของโจทย์คือ 1/x ทริคที่ช่วยทำเร็วเวลาเจอโจทย์ “tan หายังไง” ในห้องสอบ - ถ้าเห็นรูป (tanA − tanB)/(1+tanA tanB) ให้คิดเป็น tan(A−B) ก่อนเสมอ - ถ้าเห็น (tanA + tanB)/(1−tanA tanB) ให้คิดเป็น tan(A+B) - เจอมุมแปลก ๆ เช่น 188°, 108° ไม่ต้องกลัว ให้หาผลต่าง/ผลบวกก่อน บางทีได้มุมพิเศษใกล้ 90° แล้วใช้ co-function ต่อ ลองฝึกเพิ่ม: ถ้าเปลี่ยนเป็น (tan188° + tan108°)/(1 − tan188°tan108°) จะกลายเป็น tan(296°) แล้วค่อยลดมุมด้วยคาบ 180° เพื่อเชื่อมกับ tan มุมคุ้น ๆ ได้เหมือนกันค่ะ

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