Question

Решить 1/((1-cosx)(1+cosx))=ctgx+3

Answer 1

$displaystylefrac{1}{(1-cosx)(1+cosx)}=ctgx+3\frac{1}{1-cos^2x}=ctgx+3\frac{1}{sin^2x}=ctgx+3\1+ctg^2x=ctgx+3\ctg^2x-ctgx-2=0\ctgx_1=-1;ctgx_2=2\x_1=-frac{pi}{4}+pi n;nin Z\x_2=arcctg(2)+pi n;nin Z$