tan60=2 tan30/1-tan^2 30

sqrt(3)=I'm confused of that 2 but i guess it means to multiply.
again..
sqrt(3)= (2) sqrt(3)/3 / 1- sqrt(3)/2 ^2
now i don't know how to square tan .
if u can show me in details i would appreciate it. this is just a practice problem and i want to learn it so i can do the exam problem on my own.

looks like you are verfying the formula

tan (2A) = 2tanA/(1 - tan^2 A) , using A = 30°

so your left side = √3 , leave it alone

Right Side = (2√3/3) / (1- (√3/3)^2)
= (2√3/3) / ( 1 - 1/3)
= (2√3/3)/(2/3
= (2√3/3)(3/2) = √3 = left side

To solve the equation tan60 = (2 tan30) / (1 - tan^2 30), let's break it down step by step:

Step 1: Convert the angles to degrees or radians (depending on the given format). In this case, tan60 and tan30 are generally given in degrees.

Step 2: Determine the values of tan60 and tan30.
- tan60 = √3
- tan30 = 1/√3 or √3/3

Step 3: Substitute the values of tan60 and tan30 into the equation.
√3 = (2 * √3/3) / (1 - (√3/3)^2)

Step 4: Simplify the equation.
√3 = (2 * √3/3) / (1 - 3/9)
√3 = (2 * √3/3) / (1 - 1/3)
√3 = (2 * √3/3) / (2/3)
√3 = √3

Step 5: Verify the answer.
Since both sides of the equation are equal, this confirms that the equation is true.

Regarding your question about squaring tan:
To square tan, you need to square the entire expression of tan, including any coefficients or variables attached to it. For example, (2tan30)^2 would be equal to (2^2)(tan30^2) = 4(tan30^2).

In this case, the equation does not require squaring tan. We only need to simplify the terms using the given values of tan30 and tan60.

I hope this explanation helps! Let me know if you have any further questions.