Question

How do you solve \[6ta{n^2}x - 2 = 0\] ?

Answer 1

Hint: In the given question, we have been asked to find the value of ‘x’ and it is given that \[6ta{n^2}x - 2 = 0\] . To solve this question, we need to get ‘x’ on one side of the “equals” sign, and all the other numbers on the other side. To solve this equation for a given variable ‘x’, we have to undo the mathematical operations such as addition, subtraction, multiplication, and division that have been done to the variables.

Complete step-by-step answer:
We have given that,
 \[6ta{n^2}x - 2 = 0\]
Now, add $2$ both the side of the equation, we will get the following result ,
 \[6ta{n^2}x = 2\]
Now, divide the equation by $6$ , we will get ,
 \[ta{n^2}x = \dfrac{2}{6}\]
Now, simplify the above equation as ,
 \[ta{n^2}x = \dfrac{1}{3}\]
Taking square root both the side, we will get the following result ,
 \[tanx = \pm \dfrac{1}{{\sqrt 3 }}\]
Now, we have
 \[tanx = \dfrac{1}{{\sqrt 3 }}\]
For this we know that
 \[x = \dfrac{\pi }{3} + k\pi \]
And we also have
  \[tanx = - \dfrac{1}{{\sqrt 3 }}\]
For this we also know that
 \[x = - \dfrac{\pi }{3} + k\pi \]
Therefore, we have the combined result as
 \[x = \pm \dfrac{\pi }{3} + k\pi \]
Hence, we get our required result.
So, the correct answer is “ \[x = \pm \dfrac{\pi }{3} + k\pi \] ”.

Note: In order to solve and simplify the given expression we have to use the identities and express our given expression in the simplest form and thereby solve it. The important thing to recollect about any equation is that the ‘equals’ sign represents a balance. What the sign says is that what’s on the left-hand side is strictly an equal to what’s on the right-hand side. It is the type of question mathematical operations such as addition, subtraction, multiplication and division are used.