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cos2x/cosx = 2cosx - 1/cosx
d/dx 2 cos x = -2 sin x
(1-cosx)/sinx + sinx/(1- cosx) = [(1 - cosx)*(1 - cosx) + sinx*sinx]/[sinx*(1-cosx)] = [1 - 2cosx + cos2x + sin2x]/[sinx*(1-cosx)] = [2 - 2cosx]/[sinx*(1-cosx)] = [2*(1-cosx)]/[sinx*(1-cosx)] = 2/sinx = 2cosecx
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SinX + Sin2X = 0 SinX + 2SinXCosX = 0 Factor SinX(1 - 2CosX) = 0 Hence SinX = 0 X = = 0 , 180, 360, .... & 1 - 2CosX = 0 2CosX = 1 Cos X = 1/2 = 0.5 X = 60, 240, 420, ....
d/dx 2 cos x = -2 sin x
cos2x/cosx = 2cosx - 1/cosx
take out the constant -2 then take the intergral of cosx this will give you sinx your answer is -2sinx
30 degrees explanation 2Cosx-radical 3=0 Then 2cosx=radical 3 and cos x=(radical 3)/2 Now remember that cos 300 is (radical 3)/2 from the 30/60/90 triangle. So the answer is 30 degrees.
tanx=2cscx sinx/cosx=2/sinx sin2x/cosx=2 sin2x=2cosx 1-cos2x=2cosx 0=cos2x+2cosx-1 Quadratic formula: cosx=(-2±√(2^2+4))/2 cosx=(-2±√8)/2 cosx=(-2±2√2)/2 cosx=-1±√2 cosx=approximately -2.41 or approximately 0.41. Since the range of the cosine function is [-1,1], only approx. 0.41 works. So: cosx= approx. 0.41 Need calculator now (I went as far as I could without one!) x=approx 1.148
(1-cosx)/sinx + sinx/(1- cosx) = [(1 - cosx)*(1 - cosx) + sinx*sinx]/[sinx*(1-cosx)] = [1 - 2cosx + cos2x + sin2x]/[sinx*(1-cosx)] = [2 - 2cosx]/[sinx*(1-cosx)] = [2*(1-cosx)]/[sinx*(1-cosx)] = 2/sinx = 2cosecx
2cos2x - cosx -1 = 0 Factor: (2cosx + 1)(cosx - 1) = 0 cosx = {-.5, 1} x = {...0, 120, 240, 360,...} degrees
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For f(x) + g(x), the derivative d/dx[f(x) + g(x)] = f'(x) + g'(x). Essentially, this just means that since it's addition, you can take the derivative of each part.d/dx(x - 2cosx) =* d/dx is a way to indicate you're taking the derivatived/dx(x) + d/dx(-2cosx)* take the derivative of each part, distributing(1) + (-2*-sinx)* f(x) = x, f'(x) = 1 & g(x) = -2cosx, g'(x) = +2sinx= 1 + 2sinx
To solve this equation, you must first put the equation in terms of cosx.3cosx=2cosx = 2/3Next, you find the reference angle (α) by finding the cos inverse of 2/3.α=cos-1(2/3) = 48.19 Degrees (approximately)find the distance from from 48.19 and 90 you then add the difference to 270 giving you the two answers which are ... 48.19 and 311.81 (approximately)