2
A=\(1+\dfrac{2cot35}{cot35}\)=1+2=3
3.
tanx=3\(\Rightarrow\)\(\dfrac{sinx}{cosx}=3\Rightarrow sinx=3cosx\)
\(A=\dfrac{\left(3cosx\right)^3-cos^3x}{\left(3cosx\right)^3+cos^3x}\)=\(\dfrac{27cos^3x-cos^3x}{27cos^3x+cos^3x}=\dfrac{26cos^3x}{28cos^3x}\)=\(\dfrac{26}{28}=\dfrac{13}{4}\)
\(2,\\ A=\left(\sin^272^0+\cos^272^0\right)+\dfrac{2\cot35^0}{\cot35^0}=1+2=3\\ 3,\\ 1+\tan^2x=\dfrac{1}{\cos^2x}\Leftrightarrow10=\dfrac{1}{\cos^2x}\Leftrightarrow\cos^2x=\dfrac{1}{10}\\ \Leftrightarrow\cos x=\dfrac{\sqrt{10}}{10}\Leftrightarrow\cos^3x=\dfrac{\sqrt{10}}{100}\)
Mà \(\tan x=\dfrac{\sin x}{\cos x}\Leftrightarrow\sin x=3\cdot\dfrac{\sqrt{10}}{10}=\dfrac{3\sqrt{10}}{10}\)
\(\Leftrightarrow\sin^3x=\dfrac{27\sqrt{10}}{100}\)
\(A=\dfrac{\sin^3x-\cos^3x}{\sin^3x+\cos^3x}=\dfrac{26\sqrt{10}}{100}:\dfrac{28\sqrt{10}}{100}=\dfrac{13}{14}\)
