MATHEMATICS M2 QUESTION @ 百科全書

標題:

MATHEMATICS M2 QUESTION

發問:

25. In the figure, ABC is an equilateral triangle of sides x. P, Q and R are the feet if the perpendicular of A, B and C to DE respectively, DAB is a straight line and angle ADE = θ where π/ 6 < θ < π/ 2.圖片參考：http://imgcld.yimg.com/8/n/HA00610265/o/701004020028013873372260.jpga) Prove that i) PR =... 顯示更多 25. In the figure, ABC is an equilateral triangle of sides x. P, Q and R are the feet if the perpendicular of A, B and C to DE respectively, DAB is a straight line and angle ADE = θ where π/ 6 < θ < π/ 2. 圖片參考：http://imgcld.yimg.com/8/n/HA00610265/o/701004020028013873372260.jpg a) Prove that i) PR = x cose (π/3 - θ) ii) PQ = x cos θ iii) QR = x cose (2π/3 - θ) b) using the result of a) , prove that cos θ + cos θ( 2π/3 - θ) = cos (π/3 - θ) c) Using the above results and putting θ = π/4, prove that i) cos π/12 - sin π/12 = √ 2 /2. ii) cos π /12 + sin π /12 = √6/2. d) Hence, find the value of sec π /12.

最佳解答:

http://img97.imageshack.us/img97/3831/41403284.png cii 極其量想到 √6 = √(3x2) 我猜跟 cos30 有關但沒hint應該做不了 2010-04-03 08:23:52 補充：原來立刻應用ci，感謝 nelsonywm2000 的意見 cii 部份： http://img89.imageshack.us/img89/6295/41456663.png (由nelsonywm2000提供)