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Amath Trigo
Find the general solutions of the following equations in degrees 1) tanx+tan(45+x)=2 2) 2sinx+3cotx=3+2cosx
最佳解答:
1)tan x + tan(45+x) = 2 tanx + (tan45 + tanx)/(1﹣tan45tanx) = 2 tanx(1﹣tan45tanx) + tan45 + tanx = 2(1﹣tan45tanx) tanx﹣ tan2x + 1 + tanx = 2(1﹣tanx) 2tanx﹣tan2x + 1 = 2﹣2tanx tan2x﹣4tanx + 1 = 0 tanx = {4±√[42﹣4(1)]}/2 = 2±√3 tanx = 2+√3 OR tanx = 2﹣√3 x = 180on + 75o OR x = 180on + 15o, where n is an integer 2) 2sinx + 3cotx = 3 + 2cosx 2sin2x + 3cosx = 3sinx + 2 sinx cosx 3cosx﹣2 sinx cosx = 3sinx﹣2sin2x cosx(3﹣2 sinx) = sinx(3﹣2 sinx) (3﹣2 sinx)(sinx﹣cosx) = 0 sinx = 2/3 or tanx = 1 x = 180no + (-1)n 41.8o OR 180no+ 45o, where n is an integer
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Amath Trigo
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發問:Find the general solutions of the following equations in degrees 1) tanx+tan(45+x)=2 2) 2sinx+3cotx=3+2cosx
最佳解答:
1)tan x + tan(45+x) = 2 tanx + (tan45 + tanx)/(1﹣tan45tanx) = 2 tanx(1﹣tan45tanx) + tan45 + tanx = 2(1﹣tan45tanx) tanx﹣ tan2x + 1 + tanx = 2(1﹣tanx) 2tanx﹣tan2x + 1 = 2﹣2tanx tan2x﹣4tanx + 1 = 0 tanx = {4±√[42﹣4(1)]}/2 = 2±√3 tanx = 2+√3 OR tanx = 2﹣√3 x = 180on + 75o OR x = 180on + 15o, where n is an integer 2) 2sinx + 3cotx = 3 + 2cosx 2sin2x + 3cosx = 3sinx + 2 sinx cosx 3cosx﹣2 sinx cosx = 3sinx﹣2sin2x cosx(3﹣2 sinx) = sinx(3﹣2 sinx) (3﹣2 sinx)(sinx﹣cosx) = 0 sinx = 2/3 or tanx = 1 x = 180no + (-1)n 41.8o OR 180no+ 45o, where n is an integer
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