bất phương trình lượng giác

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duyanhkt

đặt [tex]\Large\leftarrow^{\text{u}}=(2cosxcosy;sin(x-y))[/tex] và [tex]\Large\leftarrow^{\text{v}}={2sinxsiny;sin(x-y)[/tex] [tex]\sqrt{4cos^2xcos^2y+sin^2(x-y)}+ \sqrt{4sin^2xsin^2y+sin^2(x-y)}=|\Large\leftarrow^{\text{u}}|+ |\Large\leftarrow^{\text{v}}| \ge \ |\Large\leftarrow^{\text{u}} + \Large\leftarrow^{\text{v}}|=\sqrt{(2cosxcosy+2sinxsiny)^2 + (sin(x-y)+sin(x-y))^2}=2\sqrt{cos^2(x-y)+sin^2(x-y)}=2[/tex]
[tex]\Large\leftarrow^{\text{u}}[/tex] là vecto u
 
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