SOLUTION: Evaluate sin2x + cos2x when tanx = -2

Use the formulas of half argument written for 2x and x:


sin(2x) = ,  cos(2x) = .


For these formulas see, for example, the lesson
    - FORMULAS FOR TRIGONOMETRIC FUNCTIONS 
in this site.


By applying them, you will get

sin(2x) + cos(2x) =  +  =  = .


Answer.  .