1. ## Trig equation

sin(x+45) + sin(s-45)=sqrt(2)

sin(x+45) + sin(s-45)=sqrt(2)
try using the sum and difference identities for sine

$\sin(x+y)=\sin(x)\cos(y)+\sin(y)\cos(x)$

$\sin(x-y)=\sin(x)\cos(y)-\sin(y)\cos(x)$

This gives

$
\sin(x)\cos(45)+\sin(45)\cos(x)+\sin(x)\cos(45)-\sin(45)\cos(x)=\sqrt{2}
$

Can you finish from here?

Good luck

3. Thanks very much, yes I can do it now