Find the general form of the solution of the equation x such that sin x = cos5x. Example: for the equation tan x=1, the solutions can be described by x = pi/4 + n*pi, nEZ
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Expert's answer
2010-06-09T07:34:09-0400
sin x = cos5x sin x = cos(pi/2 - x) cos(pi/2 - x) = cos(5x) cos(pi/2 - x) - cos(5x) = 0 -2sin(( pi/2-x+5x)/2 ) sin ((pi/2-x-5x)/2)=0 -2sin (pi/4+2x) sin (pi/4 -3x)= 0 х=pi*n/2-pi/8 or х=pi/12-pi*n/3, nEZ
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