Question

cos(2*x)=sin(x-90)-1

Answer 1

$cos(2x)=sin(x-90)-1 \\ cos(2x)=-cosx-1 \\ cos^2x-sin^2x=-cosx-cos^2x-sin^2x \\ 2cos^2x+cosx=0 \\ cosx(2cosx+1)=0 \\ \\ cosx=0 \\ x= \frac{ \pi }{2} + \pi k \\ \\ cosx=- \frac{1}{2} \\ x=б \frac{2 \pi }{3} +2 \pi k$