Question

cos x/ 1-cos x - 1/ cos x = -1

Answer 1

$\frac{cos x}{1-cos x} - \frac{1}{cos x} =-1 \\ \\ cos x=u \\ \\ \frac{u}{1-u} - \frac{1}{u} =-1 \\ \\ u(1-u) \frac{u}{(1-u)} -u(1-u) \frac{1}{u} =-1[u(1-u)] \\ \\ u^2-1+u=-1[u-u^2] \\ \\ u^2-1+u=-u+u^2 \\ \\ u^2-u^2+u+u=1 \\ \\ 2u=1 \\ \\ u= \frac{1}{2} \\ \\ \\ cos x= \frac{1}{2} \\ \\ \\ x= \frac{ \pi }{3} +2 \pi k \\ \\ \\ x= \frac{5x}{3} +2 \pi k$