已知3sinA+5sinA=5 求3sinA-5cosA=

已知3sinA+5cosA=5 求3sinA-5cosA=?
将3sinA+5cosA=5得：sinA=(5-5cosA)/3
代入sin^A+cos^A=1得:[(5-5cosA)/3]^+cos^A=1

25-50cosA+25cos^A+9cos^A=9
34cos^A-50cosA+16=0
17cos^A-25cosA+8=0
(17cosA-8)(cosA-1)=0
cosA=8/17 OR cosA=1
if cosA=8/17, sinA=15/17 3sinA-5cosA=3*15/17-5*8/17=5/17
if cosA=1,sinA=0，3sinA-5cosA=3*0-5*1=-5

已知3sinA+5sinA=5 求3sinA-5cosA=?

估计你题目写错了， 应该是 3sinA + 5cosA = 5, 否则如果是 3sinA+5sinA=5 ， 那就是 8sinA = 5, sina = 5/8, cosA = +- (1 - (5/8)^2 )^(1/2) = +- 39^(1/2)/8
3sinA-5cosA = 15/8 +- 5*39^(1/2) / 8

解： 3sinA + 5cosA = 5
3sinA / 5 + cosA = 1
cosA = 1 - 3sinA / 5
(cosA)^2 = 1 + 9/25 * (sinA)^2 - 6sinA/5
1 - (sinA)^2 = 1 + 9/25 * (sinA)^2 - 6sinA/5
0 = 17 * (sinA)^2 - 15sinA
sinA * (17sinA - 15) = 0
sinA = 0 或 sinA = 15/17

当 sinA = 0, cosA = 1
3sinA-5cosA = - 5

当 sinA = 15/17， cosA = 1 - 3/5 * 15/17 = 8/17
3sinA-5cosA = 3*15/17 - 5*8/