Question

Решите тригонометрические уравнение cos3x=2sin3π/2+x

Answer 1

$cos 3x=2sin( frac{3 pi }{2} +x)\ \ cos3x = -2cos x\ \ cos3x+cos x+cos x=0\ \ 2cos2xcos x+cos x=0\ \ cos x(2cos 2x+1)=0\ \ left[begin{array}{ccc}cos x=0\ cos 2x=-0.5end{array}rightRightarrow~~~ left[begin{array}{ccc}x_1= frac{pi}{2}+ pi n,n in mathbb{Z}\ x_2=pm frac{pi}{3}+ pi n,n in mathbb{Z} end{array}right$