Question

Are there any solutions for this equation within (0,2π)? [cosx=sinx] if so, what are they?

Answer 1

`x=pi/4, (5pi)/4`

Explanation:

Examining the unit circle, we see where `cosx=sinx`, or where `(x,y)=(x,x)`:

`x=pi/4, (5pi)/4`

It does not hold true in the other quadrants (quadrants II, IV), as the sine and cosine have opposite signs for all angles in those quadrants.