solve this problem?

Question

(square root)3 * tan 4x + 1 = 0 solve for x

Answer 1

x = - pi / 24

Answer 2

Assuming a restriction of x in the interval [0, 2pi):

sqrt(3) (tan4x) + 1 = 0

Move the 1 over to the right hand side,

sqrt(3) tan4x = -1

Divide both sides by sqrt(3),

tan(4x) = -1/sqrt(3)

Now, where on the graph is tan equal to -1/sqrt(3)? We at least know it's going to be in quadrants 2 and 4. The answer is at 5pi/6 and 11pi/6

Therefore,

4x = {5pi/6, 11pi/6, ?, ?, ?, ?, ?, ?}

Since we have that 4x, we have to quadruple the number of solutions, hence the question marks. What we're going to have to fill the question marks are
5pi/6 + 2pi, 5pi/6 + 4pi, 5pi/6 + 6pi
11pi/6 + 2pi, 11pi/6 + 4pi, 11pi/6 + 6pi

4x = {5pi/6, 11pi/6, 17pi/6, 23pi/6, 29pi/6, 35pi/6, 41pi/6, 47pi/6}

Now, we multiply both sides by 1/4, which means all of the denominators get multiplied by 4.

x = {5pi/24, 11pi/24, 17pi/24, 23pi/24, 29pi/24, 35pi/24, 41pi/24, 47pi/24}

Answer 3

(√3) tan(4x) + 1 = 0
tan(4x) = -1/√3
4x = arctan(-1/√3) = 5π/6 + πn, where n is an interger
x = (1/4)(5π/6 + πn) = 5π/24 + πn/4 = 5π/24 + 6πn/24

Answer 4

if by this you mean

sqrt(3)(tan(4x + 1)) = 0
tan(4x + 1) = 0
4x + 1 = 0
4x = -1
x = (-1/4)

However if you mean

sqrt(3)tan(4x) + 1 = 0
sqrt(3)tan(4x) = -1
tan(4x) = -1/(sqrt(3))
tan(4x) = (-sqrt(3)/3)
4x = 330 or 150
x = 82.5 or 37.5

Answer 5

tan4x= -1/sqrt3 = tan(-pie/6)
now if
tan a=tan b
a=n*pie +b , n = an integer;
thus 4x=(n*pie - pie/6)

=> x = (1/4)(n*pie - pie/6)