SOLUTION: sinx + cosx - sinxcosx = sin^2 x + cos^2 x

Algebra ->  Trigonometry-basics -> SOLUTION: sinx + cosx - sinxcosx = sin^2 x + cos^2 x      Log On


   

Question 94923: sinx + cosx - sinxcosx = sin^2 x + cos^2 x
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
sinx + cosx - sinxcosx = sin^2 x + cos^2 x
cosx + sinx - sinxcosx = 1
cosx + sinx = 1 + sinxcosx
cos^2 x + 2cosxsinx + sin^2 x = 1 + 2sinxcosx + sin^2 x cos^2 x
cos^2 x + sin^2 x = 1 + sin^2 x cos^2 x
1 = 1 + sin^2 x cos^2 x
0 = sin^2 x cos^2 x
sin^2 x = 0
Ans: 2(pi)k
cos^2 x = 0
Ans: (pi)/2 + 2(pi)k
~k is any integer