Question

Solve: cot^2((pix)/2)=3

Answer 1

We are given the following equation:

`cot^2((\pi)/(2)x)=3`

To solve for "x" we will take the square root to both sides:

`cot((\pi)/(2)x)=√(3)`

Now, we take the inverse function of cotangent:

`(\pi)/(2)x=cot^(-1)√(2)`

Solving the operations:

`(\pi)/(2)x=(\pi)/(6)`

Now, we can cancel out the pi:

`(1)/(2)x=(1)/(6)`

Now, we multiply both sides by 2:

`x=(2)/(6)`

Simplifying:

`x=(1)/(3)`

Therefore, the value of "x" is 1/3