If $\text{'}\text{θ}\text{'}$  is the acute angle between the lines$3x+y–4=0,x+3y–4=0$ , then the value of $\text{cosθ}$ is

$a_{1}x+b_{1}y+c_1=0,a_{2}x+b_{2}y+c_2=0$

$a_1=3,b_1=1,c_1=-4,a_2=1,b_2=3,c_2=-4$

$\cos \theta =\left|\frac{a_1{a}_2+b_1{b}_2}{\sqrt{a_1{}^2+b_1{}^2}\sqrt{a_2{}^2+b_2{}^2}}\right|$

$=\left|\frac{3\times 1+1\times 3}{\sqrt{3^2+1^2}\sqrt{1^2+3^2}}\right|$

$=\left|\frac{3+3}{\sqrt{10}\sqrt{10}}\right|$

$=\left|\frac{6}{10}\right|$

$\cos \theta =\frac{3}{5}$