Giải pt Sin(pi/3 – x ) + cos(pi/3 – x ) = -1

Giải pt
Sin(pi/3 – x ) + cos(pi/3 – x ) = -1

Share

1 Answer

  1. \[\begin{array}{l}
    \sin \left( {\frac{\pi }{3} – x} \right) + \cos \left( {\frac{\pi }{3} – x} \right) = – 1\\
    \Leftrightarrow \sqrt 2 \sin \left( {\frac{\pi }{3} – x + \frac{\pi }{4}} \right) = – 1\\
    \Leftrightarrow \sin \left( {\frac{{7\pi }}{{12}} – x} \right) = – \frac{1}{{\sqrt 2 }}\\
    \Leftrightarrow \left[ \begin{array}{l}
    \frac{{7\pi }}{{12}} – x = – \frac{\pi }{4} + k2\pi \\
    \frac{{7\pi }}{{12}} – x = \frac{{5\pi }}{4} + k2\pi
    \end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
    x = \frac{{5\pi }}{6} + k2\pi \\
    x = – \frac{{2\pi }}{3} + k2\pi
    \end{array} \right.\,\,\left( {k \in Z} \right).\\
    Ap\,\,dung\,\,cong\,\,thuc:\\
    \sin \alpha + \cos \alpha = \sqrt 2 \sin \left( {\alpha + \frac{\pi }{4}} \right)\\
    Voi\,\,bai\,\,nay:\,\,\alpha = \frac{\pi }{3} – x.
    \end{array}\]

    • 0
Leave an answer

Leave an answer

Browse