`sin(x) - 2 = cos(x) - 2` Find all the solutions of the equation in the interval `0,2pi)`.

Expert Answers
gsarora17 eNotes educator| Certified Educator

`sin(x)-2=cos(x)-2`

`sin(x)-2-cos(x)+2=0` 

`sin(x)-cos(x)=0`

`(sin(x)-cos(x))/cos(x)=0`

`tan(x)-1=0`

`tan(x)=1`

General solutions for tan(x)=1 are `x=pi/4+pin`

Solutions for the range `0<=x<=2pi` are

`x=pi/4 , (5pi)/4`