cosA-cosB=1/2,sinA-sinB=-1/3,求：cos(A+B),sin(A+B)的值。
高手們,,幫幫手
數學難題..數學高手請幫手
2010-07-24 7:22 pm
回答 (1)
2010-07-24 7:40 pm
✔ 最佳答案
cosA - cosB = - 2sin (A+B)/2 sin (A-B)/2 = 1/2.....(1)sinA - sinB = 2 cos(A+B)/2 sin(A-B)/2 = - 1/3.......(2)(1) / (2) :[- 2sin (A+B)/2 ] / [2 cos(A+B)/2] = - 3/2tan (A+B)/2 = 3/2So sin(A+B)= [2 tan (A+B)/2] / [1 + tan^2 (A+B)/2] = 2(3/2) / [1 + (3/2)^2]= 12/13cos(A+B)= [1 - tan^2 (A+B)/2] / [ 1 + tan^2 (A+B)/2 ]= [1 - (3/2)^2 ] / [ 1 + (3/2)^2]= - 5/13
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