Question

For what value of `x` does `sin(x)+cos(x)=x`?

Answer 1

Assuming we are working in radians then
`color(white)("XXX")x~~1.2587`

Explanation:

I suspect this question is invalid, but in case it is not (and in order to clear it from the unanswered question list), here is what I was able to come up with:

If I graph `f(x)=sin(x)+cos(x)` and `f(x)=x`
I get an intersection point that is between `x=1.2` and `x=1.3`

Using a spreadsheet and a variant of the Newton Method I was able to approximate this more closely at about `x=1.2587`

NOTE This is not intended to be a "proper" solution. Perhaps there is some way to use the Taylor Expansion for `arctan` to get a better solution but, since I was uncertain that the question was even correct, this is the best I could do without excessive analysis.