cos3x sin2x*cosx:ctgx упростить

Question

cos3x sin2x*cosx:ctgx упростить

Comments

Такое выражение? cos(3x)*sin(2x)*cos(x) / ctg(x)

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извиняюсь знак исчезает cos(3x)+sin(2x)*cos(x) / ctg(x)

Answer 1

Cos(3x)+sin(2x)*cos(x) / ctg(x)
cos(3x)+sin(2x)*cos(x) / [cos(x)/sin(x)] =  cos(3x)+sin(2x)*cos(x)*sin(x) / cos(x) = cos(3x) + sin(x)*sin(2x) = cos(x+2x) + sin(x)*sin(2x) = cos(x)*cos(2x) - sin(x)*sin(2x) + sin(x)*sin(2x) = cos(x)*cos(2x) = cos(x)*(2cos^2(x) - 1) = 2*cos^3(x) - cos(x)

Answer 2

Cos3x+sin2x*cosx*sinx/cosx=cos3x+sin2x*cosx*sinx/cosx=cos3x+sin2xsinx=
=cos3x+1/2(cos(x)-cos3x)=1/2(cos3x+cosx)=cos2xcox