Toán Lớp 11: Giải giúp mình với, cảm ơn ạ
Cos(3x/2+pi/5)×sin(3x/2+pi/5)=√6/2
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Toán Lớp 11: Giải giúp mình với, cảm ơn ạ
Cos(3x/2+pi/5)×sin(3x/2+pi/5)=√6/2
Comments ( 1 )
\sin 2x = 2\sin x.\cos x\\
\cos \left( {\dfrac{{3x}}{2} + \dfrac{\pi }{5}} \right).\sin \left( {\dfrac{{3x}}{2} + \dfrac{\pi }{5}} \right) = \dfrac{{\sqrt 6 }}{2}\\
\Leftrightarrow \dfrac{1}{2}.\left[ {2\sin \left( {\dfrac{{3x}}{2} + \dfrac{\pi }{5}} \right).\cos \left( {\dfrac{{3x}}{2} + \dfrac{\pi }{5}} \right)} \right] = \dfrac{{\sqrt 6 }}{2}\\
\Leftrightarrow \dfrac{1}{2}.\sin \left[ {2.\left( {\dfrac{{3x}}{2} + \dfrac{\pi }{5}} \right)} \right] = \dfrac{{\sqrt 6 }}{2}\\
\Leftrightarrow \dfrac{1}{2}\sin \left( {3x + \dfrac{{2\pi }}{5}} \right) = \dfrac{{\sqrt 6 }}{2}\\
\Leftrightarrow \sin \left( {3x + \dfrac{{2\pi }}{5}} \right) = \sqrt 6 \\
– 1 \le \sin \left( {3x + \dfrac{{2\pi }}{5}} \right) \le 1 \Rightarrow Phương\,\,\,trình\,\,vô\,\,nghiệm
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