Toán Lớp 11: giải pt lượng giác
sin(x+24độ) +cos(x+144 độ)=sin15độ
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Toán Lớp 11: giải pt lượng giác
sin(x+24độ) +cos(x+144 độ)=sin15độ
Comments ( 1 )
\sin \left( {x + {{24}^o}} \right) + \cos \left( {x + {{144}^o}} \right) = \sin {15^o}\\
\Leftrightarrow \sin \left( {x + {{24}^o}} \right) + \cos \left( {{{90}^o} + {{54}^o} + x} \right) = \sin {15^o}\\
\Leftrightarrow \sin \left( {x + {{24}^o}} \right) – \sin \left( {{{54}^o} + x} \right) = \sin {15^o}\\
\Leftrightarrow 2\cos \left( {x + {{39}^o}} \right).\sin \left( { – {{15}^o}} \right) = \sin {15^o}\\
\Leftrightarrow – 2\cos \left( {x + {{39}^o}} \right).\sin {15^o} = \sin {15^o}\\
\Leftrightarrow \cos \left( {x + {{39}^o}} \right) = – \dfrac{1}{2}\\
\Leftrightarrow \left[ \begin{array}{l}
x + {39^o} = {120^o} + k{360^o}\\
x + {39^o} = – {120^o} + k{360^o}
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = {81^o} + k{360^o}\\
x = – {159^o} + k{360^o}
\end{array} \right.\left( {k \in Z} \right)
\end{array}$