Please can you help?
sin(x+45) + sin(s-45)=sqrt(2)
try using the sum and difference identities for sine
$\displaystyle \sin(x+y)=\sin(x)\cos(y)+\sin(y)\cos(x)$
$\displaystyle \sin(x-y)=\sin(x)\cos(y)-\sin(y)\cos(x)$
This gives
$\displaystyle
\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