How does this trig identity work?

[zeion]

Homework Statement

How does |sinx + cosx| = |sqrt(2)(x + (pi/4))| ?

Homework Equations

The Attempt at a Solution

Some kind of co-function identity?

 

[tiny-tim]

hi zeion!

(have a square-root: √ and a pi: π )

do you mean |sinx + cosx| = |√2 sin(x + π/4)| ?

hint: expand sin(x + π/4) ​