Question

Решить 1/((1-cosx)(1+cosx))=ctgx+3

Answer 1

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