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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) (Show Source): Answer by ikleyn(52776) (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
= 1. (2)
Take into account that + == 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 = or x = , where k is any integer number.
Checking these potential solutions, we get the final answers x = , or x = , where n is any integer number.
Of the given four optional choices, only x= 90° is the solutions to the given equation.
Solved.
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