Phương trình $\sin x + \sqrt 3 \cos x = \sqrt 2$  có hai họ nghiệm có dạng $x = \alpha  + k2\pi ,\,x = \beta  + k2\pi ,$

$\left( { - \dfrac{\pi }{2} < \alpha <\beta  < \dfrac{\pi }{2}} \right)$ . Khi đó $\alpha .\beta$ là:

$O\left( {0;0} \right)$

$M\left( {0;1} \right)$

$N\left( {\dfrac{\pi }{2};0} \right)$

$P\left( {1;0} \right)$

$y = \dfrac{\pi }{3} + k\pi \left( {k \in Z} \right)$

$x = k\pi \left( {k \in Z} \right)$

$x = \dfrac{\pi }{2} + k\pi \left( {k \in Z} \right)$

$y = \dfrac{{k\pi }}{2}\left( {k \in Z} \right)$

$m =  - 3$

$m =  - 2$      

$m = 0$

$m = 3$

$\dfrac{{2\pi }}{3}$

$\dfrac{\pi }{3}$

$\dfrac{{4\pi }}{3}$

$\dfrac{{7\pi }}{3}$

$\left[ \begin{array}{l}x = \alpha  + k\pi \\x = \pi  - \alpha  + k\pi \end{array} \right.\left( {k \in Z} \right)$    

$\left[ \begin{array}{l}x = \alpha  + k2\pi \\x = \pi  - \alpha  + k2\pi \end{array} \right.\left( {k \in Z} \right)$

$\left[ \begin{array}{l}x = \alpha  + k2\pi \\x =  - \alpha  + k2\pi \end{array} \right.\left( {k \in Z} \right)$      

$\left[ \begin{array}{l}x = \alpha  + k\pi \\x =  - \alpha  + k\pi \end{array} \right.\left( {k \in Z} \right)$

$\cos x \ne 1 \Leftrightarrow x \ne \dfrac{\pi }{2} + k\pi \left( {k \in Z} \right)$

$\cos x \ne 0 \Leftrightarrow x \ne \dfrac{\pi }{2} + k\pi \left( {k \in Z} \right)$

$\cos x \ne  - 1 \Leftrightarrow x \ne  - \dfrac{\pi }{2} + k2\pi \left( {k \in Z} \right)$    

$\cos x \ne 0 \Leftrightarrow x \ne \dfrac{\pi }{2} + k2\pi \left( {k \in Z} \right)$