Asked by help!
solve the equation
cos(x) + sin(x) = 1
cos(x) + sin(x) = 1
Answers
Answered by
Reiny
square both sides
cos^2 x + 2sinxcosx + sin^2 x = 1
1 + 2sinxcosx = 1
sin (2x) = 0
2x = 0 or 2x = π or 2x = 2π
x = 0, x = π/2, x = π
the period of sin 2x is π, so adding multiples of π will yield more answers
so in the domain 0 < x < 2π , we have
x = 0, π/2, π, 3π/2, and 2π
(or x = 0, 90, 180, 270, 360 degrees)
BUT, since we squared our equation, all answers must be checked.
A quick check with a calculator shows that
x = 0, π/2, 2π are the only solutions
verfication:
https://www.wolframalpha.com/input/?i=cos(x)+%2B+sin(x)+%3D+1+for+x+%3D+0+to+2pi
cos^2 x + 2sinxcosx + sin^2 x = 1
1 + 2sinxcosx = 1
sin (2x) = 0
2x = 0 or 2x = π or 2x = 2π
x = 0, x = π/2, x = π
the period of sin 2x is π, so adding multiples of π will yield more answers
so in the domain 0 < x < 2π , we have
x = 0, π/2, π, 3π/2, and 2π
(or x = 0, 90, 180, 270, 360 degrees)
BUT, since we squared our equation, all answers must be checked.
A quick check with a calculator shows that
x = 0, π/2, 2π are the only solutions
verfication:
https://www.wolframalpha.com/input/?i=cos(x)+%2B+sin(x)+%3D+1+for+x+%3D+0+to+2pi
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.