Question

3sin60°+xcos30°.tan45°=xcot30°

Answer 1

Answer:

x = (6$\sqrt{2}$)/(4$\sqrt{2}$ -3)

Step-by-step explanation:

sin60 degree = $\sqrt{3}$ /2

cos30 degree = 1/2

tan 45 degree =  sin45 degree / cos45 degree = ($\sqrt{2}$/2)/($\sqrt{2}$ /2) = 1

cot 30 degree = cos30 / sin30 = ($\sqrt{3}$ /2)/(1/2)  = $\sqrt{3}$

so, let us plug the above values in the given eqution and solve for x

3($\sqrt{3}$ /2 ) + x(1/2) *1 = x($\sqrt{3}$)

3($\sqrt{3}$ /2 )  = x($\sqrt{3}$) -x(1/2)

3($\sqrt{3}$ /2 )  = x(($\sqrt{3}$)-(1/2)) (by taking x as a common factor)

3($\sqrt{3}$ /2 ) = x(((2$\sqrt{3}$)-(1))/2))    (making the same common denominator

now devide both sides by (((2$\sqrt{3}$)-(1))/2))

x  = 3($\sqrt{3}$ /2 )  / (((2$\sqrt{3}$)-(1))/2))

x = 3($\sqrt{3}$ ) / ((2$\sqrt{3}$)-(1))