SOLUTION: Which of the following values of x is a solution to the equation sinx + cos x=1? x=45° x=90° x=135° x=180°

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Question 1182204: Which of the following values of x is a solution to the equation sinx + cos x=1?
x=45°
x=90°
x=135°
x=180°
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849) About Me  (Show Source):
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.

This problem was posted to the forum couple of days ago,  and I gave its full solution under this link

https://www.algebra.com/algebra/homework/Functions/Functions.faq.question.1182143.html

https://www.algebra.com/algebra/homework/Functions/Functions.faq.question.1182143.html


                For your convenience,  I  copy-paste that solution here again 


Starting from

    sin(x) + cos(x) = 1,      (1)


square both sides

    sin%5E2%28x%29+%2B+2sin%28x%29%2Acos%28x%29+%2B+cos%5E2%28x%29 = 1.      (2)



Take into account that  sin%5E2%28x%29 + cos%5E2%28x%29 == 1.


You will get then from  (2)


    2*sin(x)*cos(x) = 0,

or

      sin(x(*cos(x) = 0.


So, equation (1) implies

    sin(x) = 0  or  cos(x) = 0.


It gives  x = k%2Api  or  x = pi%2F2+%2B+k%2Api,   where k is any integer number.


Checking these potential solutions,  we get the final answers  x = 2pi%2An,  or  x = pi%2F2+%2B+2pi%2An,  where n is any integer number.


Of the given four optional choices,  only  x= 90°  is the solutions to the given equation.

Solved.