Chapter 6 - Section 6.2 - More on Trigonometric Equations - 6.2 Problem Set - Page 332: 27

$x=\{\frac{\pi}{4}\}$

$sin(x)+cos(x)=\sqrt{2}$ $(sin(x)+cos(x))^2=(\sqrt{2})^2\;\;\;\;\;\;\;\;\;\;$ $sin^2(x)+2sin(x)cos(x)+cos^2(x)=2\;\;\;\;\;\;\;\;\;\;\;\;$ $2sin(x)cos(x)+1=2$ $sin(2x)=1$ $2x= sin^{-1}(1)$ $2x=\frac{\pi}{2}\;\;\;\;\;\;\;\;\;\;\;\;\;\;$ Divided each side by $2$ $x=\frac{\pi}{4}$ $x=\{\frac{\pi}{4}\}$