Question

Cos2x + sin( x - (5pi/2)) +1=0

Answer 1

`cos(2x)+sin(x- (5 \pi )/(2) )+1=0 \\ \\ cos(2x)=2cos^2(x)-1 \\ sin(x- (5 \pi )/(2) )= -cos(x) \\ \\ 2cos^2(x)-1 -cos(x) +1=0 \\ 2cos^2(x) -cos(x)=0 \\ cos(x)(2cos(x)-1)=0 \\ \\ cos(x)=0 \\ x= ( \pi )/(2) + \pi k,~~~k \in Z \\`


`\\ 2cos(x)-1=0 \\ 2cos(x)=1 \\ cos(x)= (1)/(2) \\ x= \pm ( \pi )/(3) +2 \pi k,~~k \in Z`