`(1 + cos x)(1 + sin x) = 2`
`<=> 1 + sin x + cos x + sin x.cos x = 2`
`<=> sin x + cos x + sin x.cos x = 1`
Đặt `t = sin x + cos x` `(t^2 <= 2)`
`=> 2sin x.cos x = t^2 - 1`
`=> sin x.cos x = (t^2 - 1)/2`
`PT`
`=> t + (t^2 - 1)/2 = 1`
`=> 2t + t^2 - 1 = 2`
`<=> t^2 + 2t - 3 = 0`
`<=>` \(\left[ \begin{array}{l}t = 1\\t = -3 (l)\end{array} \right.\)
`<=> 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)`
