SOLUTION: How do you solve the equation: sin + cos = sqrt2?

Algebra ->  Trigonometry-basics -> SOLUTION: How do you solve the equation: sin + cos = sqrt2?      Log On


   

Question 731290: How do you solve the equation: sin + cos = sqrt2?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
sin%28theta%29%2Bcos%28theta%29=sqrt%282%29
%28sin%28theta%29%2Bcos%28theta%29%29%5E2=2
sin%5E2%28theta%29%2Bcos%5E2%28theta%29%2B2sin%28theta%29%2Acos%28theta%29=2
1%2B2sin%28theta%29%2Acos%28theta%29=2
Using one of the trigonometric identities:
1%2Bsin%282theta%29=2
sin%282theta%29=1 --> 2theta=90%5Eo --> highlight%28theta=45%5E0%29