Form 4 QUESTIONS@2

2008-05-28 4:40 am

1.find the real roots of the equation 5/(x+1) -4/(x-2)=6
2.If cosA=-12/13 and sinB=15/17 where AB is bigger than 90° and smaller than 180°,witnout using calculators,find the values of the following:
a) sinA b)cosAcosB+sinAsinB

回答 (1)

Wan Chak

2008-05-28 5:05 am

✔ 最佳答案

1)
5/(x+1) - 4/(x-2) = 6
5(x-2) - 4(x+1) = 6(x+1)(x-2)
5x - 10 - 4x - 4 = 6(x2 - 2x + x - 2)
x - 14 = 6x2 - 6x - 12
6x2 - 7x + 2 = 0
(3x - 2)(2x - 1) = 0
x = 2/3 or x = 1/2

2a)
cosA = -12/13
cos2A = 144/169
1-cos2A = 25/169
sin2A = 25/169
sinA = 5/13 or sinA = -5/13 (rejected, as when A is bigger than 90 and smaller than 180, sinA is positive.)
therefore, sinA = 5/13//

2b)
sinB = 15/17
sin2B = 225/289
1-sin2B = 64/289
cos2B = 64/289
cosB = -8/17 or cosB = 8/17 (rejected, as when B is bigger than 90 and smaller than 180, cosA is negative)
Therefore, cosB = -8/17

cosAcosB + sinAsinB
= (-12/13)(-8/17) + (5/13)(15/17)
= 96/221 + 75/221
= 171/221//

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