Answer:
x = (6[tex]\sqrt{2}[/tex])/(4[tex]\sqrt{2}[/tex] -3)
Step-by-step explanation:
sin60 degree = [tex]\sqrt{3}[/tex] /2
cos30 degree = 1/2
tan 45 degree = sin45 degree / cos45 degree = ([tex]\sqrt{2}[/tex]/2)/([tex]\sqrt{2}[/tex] /2) = 1
cot 30 degree = cos30 / sin30 = ([tex]\sqrt{3}[/tex] /2)/(1/2) = [tex]\sqrt{3}[/tex]
so, let us plug the above values in the given eqution and solve for x
3([tex]\sqrt{3}[/tex] /2 ) + x(1/2) *1 = x([tex]\sqrt{3}[/tex])
3([tex]\sqrt{3}[/tex] /2 ) = x([tex]\sqrt{3}[/tex]) -x(1/2)
3([tex]\sqrt{3}[/tex] /2 ) = x(([tex]\sqrt{3}[/tex])-(1/2)) (by taking x as a common factor)
3([tex]\sqrt{3}[/tex] /2 ) = x(((2[tex]\sqrt{3}[/tex])-(1))/2)) (making the same common denominator
now devide both sides by (((2[tex]\sqrt{3}[/tex])-(1))/2))
x = 3([tex]\sqrt{3}[/tex] /2 ) / (((2[tex]\sqrt{3}[/tex])-(1))/2))
x = 3([tex]\sqrt{3}[/tex] ) / ((2[tex]\sqrt{3}[/tex])-(1))
