Find all solutions to sinx - cosx = sqrt(2) (1 Viewer)

[tanna]

when 0 < x < 2pi

 

[Dumbledore]

use the auxillery/subsiderary angle method thingy
a cos x + b sin x = Rsin(x+@)

in this case R will be sqrt(2) which will cancel with RHS and then its standard

 

[tanna]

oh right. thanks a lot

 

[gurmies]

An alternative would be to square both sides. Keep in mind this method introduces new "answers" which don't solve the initial equation. Make sure at the end you test if you choose to use this method (it's often quicker).