SOLUTION: Solve the equation algebraically for "x" where 0&#8804;x<2&#960;. sinx + cosx = 1 Thank you

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Question 359681: Solve the equation algebraically for "x" where 0≤x<2π.
sinx + cosx = 1

Thank you
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
sin%28x%29%2Bcos%28x%29=1
sin%28x%29=1-cos%28x%29
%28sin%28x%29%29%5E2=%281-cos%28x%29%29%5E2
1-%28cos%28x%29%29%5E2=1-2cos%28x%29%2Bcos%28x%29%5E2
2%28cos%28x%29%29%5E2-2cos%28x%29=0
cos%28x%29%2A%28cos%28x%29-1%29=0
Two solutions:
cos%28x%29=0
x=pi%2F2 and x=%283pi%29%2F2
However at x=%283pi%29%2F2, sin%28x%29=-1 and cos%28x%29=0
so that sin%28x%29%2Bcos%28x%29%3C%3E1
Only highlight%28x=pi%2F2%29 is a valid solution.
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cos%28x%29-1=0
cos%28x%29=1
highlight%28x=0%29