Tính giá trị biểu thức lượng giác

T

tuyn

Ta có: [TEX]sin3x=3sinx-4sin^3x,cos3x=4cos^3x-3cosx \Rightarrow tan3x=\frac{3tanx-tan^3x}{1-3tan^2x} [/TEX]
[TEX]\Rightarrow tan60^o=\frac{3tan20^o-tan^320^o}{1-3tan^220^o} [/TEX]
[TEX]\Leftrightarrow 3tan20^o-tan^320^o=\sqrt{3}.(1-3tan^220^o)[/TEX]
[TEX]\Rightarrow (3tan20^o-tan^320^o)^2=3(1-3tan^220^o)^2 \Leftrightarrow 9tan^220^o-6tan^420^o+tan^620^o=3-18tan^220^o+27tan^420^o[/TEX]
[TEX]\Leftrightarrow tan^620^o-33tan^420^o+27tan^220^o-3=0 \Rightarrow DPCM[/TEX]
 
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