`sin x + cos x = 1`
`<=> 1/(\sqrt{2})sin x + 1/(\sqrt{2})cos x = 1/(\sqrt{2})`
`<=> sin (x + π/4) = (\sqrt{2})/2`
`<=>` \(\left[ \begin{array}{l}x + \dfrac{π}{4} = \dfrac{π}{4} + k2π\\x + \dfrac{π}{4} = \dfrac{3π}{4} + k2π\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}x = k2π\\x = \dfrac{π}{2} + k2π\end{array} \right.\) `(k in ZZ)`
`=>` \(\left\{ \begin{array}{l}a = 0\\b = \dfrac{π}{2}\end{array} \right.\)
`=> a + b = π/2`