Question

Find an angle
x where sin x = COS x.

Answer 1

`x = \frac \pi4 + k\pi (k \in \mathbb{Z})`

Explanation:

If
`cos\ x = 0 \rightarrow sin\ x = \pm1`, which is obviously not a solution. At this point we can divide both sides by
`cos\ x` to get

`\frac {sin\ x}{cos\ x} = 1 \rightarrow tan\ x = 1`

which has solutions
`x = \frac \pi4 + k\pi (k \in \mathbb{Z})`