Question

How do you solve `sin(x) = cos(x)`?

Answer 1

`pi/4`

Explanation:

`sin x = cos (pi/2 - x)` --> complementary arcs
Therefor,
`cos (pi/2 - x) = cos x`
`(pi/2 - x) = +- x`
a. `pi/2 - x = x` --> `2x = pi/2` --> `x = pi/4`
b. `pi/2 - x = - x` (undetermined)
Answer: `x = pi/4`
Check.
`x = pi/4` --> `sin x = cos x = sqrt2/2.` OK

Answer 2

General solution of `sinx=cosx` is `x=npi+pi/4`, where `n` is an integer.

Explanation:

Dividing the equation `sinx=cosx`, by `sinx` on both sides

`sinx/cosx=1` or

`tanx=1=tan(pi/4)`

Hence, general solution of `sinx=cosx` is `x=npi+pi/4`, where `n` is an integer.