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dùng ông thức hạ bậc
cos2a=\(\dfrac{1+cos2a}{2}\)
pt<=>1+cos(4x+\(\dfrac{2\Pi}{3}\))-3sin(2x+\(\dfrac{5\Pi}{6}\))+1=0
<=>-\(\dfrac{1}{2}\)cos4x-\(\dfrac{\sqrt{3}}{2}\)sin4x+\(\dfrac{3\sqrt{3}}{2}\)sin2x-\(\dfrac{3}{2}\)cos2x+2=0
<=>(-\(\dfrac{1}{2}\)cos4x+\(\dfrac{3\sqrt{3}}{2}\)sin2x+2)+(-\(\sqrt{3}\)sin2x.cos2x-\(\dfrac{3}{2}\)cos2x)=0
<=>[-\(\dfrac{1}{2}\)(1-2sin22x)+\(\dfrac{3\sqrt{3}}{2}\)sin2x+2)-cos2x.(\(\sqrt{3}\)sin2x+\(\dfrac{3}{2}\))=0
<=>(sin22x+\(\dfrac{3\sqrt{3}}{2}\)sin2x+\(\dfrac{3}{2}\))-cos2x.(\(\sqrt{3}\)sin2x+\(\dfrac{3}{2}\))=0
<=>(sin2x+\(\dfrac{\sqrt{3}}{2}\))(sin2x+\(\sqrt{3}\))-cos2x.(sin2x+\(\dfrac{\sqrt{3}}{2}\))=0
<=>(sin2x+\(\dfrac{\sqrt{3}}{2}\))(sin2x-cos2x+\(\sqrt{3}\))=0
tới đây bạn tự giải nhé
2, \(\mathop {\lim }\limits\frac{1+2+2^2+...+2^n}{1+3+3^2+...+3^n}=\mathop {\lim }\limits\frac{\dfrac{2^{n+1}-1}{2-1}}{\dfrac{3^{n+1}-1}{3-1}}=2.\mathop {\lim }\limits\dfrac{2^{n+1}-1}{3^{n+1}-1}=2.\mathop {\lim }\limits\frac{\left (\dfrac{2}{3} \right )^{n+1}-\dfrac{1}{3^{n+1}}}{1-\dfrac{1}{3^{n+1}}}=2.0=0\)
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