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f.4 maths

發問:

1.3cos x-5sin x=-cos x +sin x 2.3tan x +5/4-tan x=2 3.tan^2x-tan x=2 4.3cos^2x-sin x-3=0 5.given that tan x=1+cos x/2sin x. a.3cos^2x+cos x-2=0 b.tan x=1+cos x/2sin x

最佳解答:

1)3cosx ﹣4sinx = -cosx + sinx 3cosx + cosx = sinx + 4sinx 4cosx = 5sinx 4 / 5 = sinx / cosx tanx = 4/5 x = 38.7 or 218.7 2)3tan x + (5/4) ﹣tan x = 2 2tan x + (5/4) = 2 2tan x = 3 / 4 tanx = 3 / 8 x = 20.6 or 200.6 3)tan2x ﹣tan x = 2 tan2x ﹣tan x ﹣2 = 0 (tanx ﹣2)(tanx + 1) = 0 tanx = 2 or tanx = -1 x = 63.4,243.4 or x = 135,315 x = 63.4,135,243.4,315 4)3cos2x ﹣sin x ﹣3 = 0 3(1 ﹣sin2x) ﹣sin x ﹣3 = 0 3 ﹣3sin2x ﹣sin x ﹣3 = 0 -3sin2x ﹣sin x = 0 3sin2x + sin x = 0 sinx(3sinx + 1) = 0 sinx = 0 or 3sinx + 1 = 0 x = 0,180,360 or x = 199.5,341.6 x = 0,180,199.5,341.6,360 5a)3cos2x + cos x ﹣2 = 0 (3cosx ﹣2)(cosx + 1) = 0 3cosx ﹣2 = 0 or cosx + 1 = 0 cosx = 2 / 3 or cosx = -1 x = 48.2,311.8 or x = 180 x = 48.2,180,311.8 5b)tan x = (1 + cos x) / 2sin x sinx/cosx = (1 + cos x) / 2sin x sinx(sinx) = cosx(1 + cos x) sin2x = cosx + cos2x 1 ﹣cos2x = cosx + cos2x 2cos2x + cosx ﹣1 = 0 (2cosx ﹣1)(cosx + 1) = 0 2cosx ﹣1 = 0 or cosx + 1 = 0 cosx = 1/2 or cosx = -1 x = 60,300 or 180 x = 60,180,300

其他解答:FAD2A23AB937987B
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