Question

3sin60°+xcos30°.tan45°=xcot30°

Answer 1

x = (6
`√(2)`)/(4
`√(2)` -3)

Explanation:

sin60 degree =
`√(3)` /2

cos30 degree = 1/2

tan 45 degree = sin45 degree / cos45 degree = (
`√(2)`/2)/(
`√(2)` /2) = 1

cot 30 degree = cos30 / sin30 = (
`√(3)` /2)/(1/2) =
`√(3)`

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

3(
`√(3)` /2 ) + x(1/2) *1 = x(
`√(3)`)

3(
`√(3)` /2 ) = x(
`√(3)`) -x(1/2)

3(
`√(3)` /2 ) = x((
`√(3)`)-(1/2)) (by taking x as a common factor)

3(
`√(3)` /2 ) = x(((2
`√(3)`)-(1))/2)) (making the same common denominator

now devide both sides by (((2
`√(3)`)-(1))/2))

x = 3(
`√(3)` /2 ) / (((2
`√(3)`)-(1))/2))

x = 3(
`√(3)` ) / ((2
`√(3)`)-(1))