Question

How do you solve `cosx=sinx` and find all exact general solutions?

Answer 1

`x = pi/4 + 2kpi`

Explanation:

cos x = sin x
Property of complementary arcs -->
`cos x = sin (pi/2 - x)`
There for:
sin x = sin (pi/2 - x)
There are 2 solutions:
a. `x = pi/2 - x` --> `2x = pi/2` --> `x = pi/4`
b. `x = pi - (pi/2 - x) = pi/2 + x`
Undefined equation .
General answer:
`x = pi/4 + 2kpi`