for tan2x=3 i get should get two values 71.56 and 251.56 but i dnt knw how to solve to get this two values. pls help me with this. thanx in advance.

reason it this way

let 2x = Ø
then tanØ = 3
Ø must be in quadrants I or III
and using your calculator
Ø = 79.52° or 180+79.52 = 259.52°

then 2x = 79.52 or 2x = 259.52
x=39.76° or x = 129.76°

check:
tan(2x39.76) = tan 79.52 = 3
same for the other one.

I don't know how "they" got your answers.

Sorry your numbers were correct, had my calculator set to GRAD, how silly of me.

Just change my numbers, the method is correct.

To find the two values for which tan(2x) equals 3, you need to solve the equation for x. Here's how you do it:

1. Take the inverse tangent (arctan) of both sides of the equation to isolate the variable x:
arctan(tan(2x)) = arctan(3)

2. Since tan(2x) is positive for both positive and negative values of x, we don't need to consider quadrants.

3. Apply the double-angle formula for tangent to simplify the equation:
2x = arctan(3)

4. Divide both sides by 2 to solve for x:
x = (1/2) * arctan(3)

5. Use a calculator to evaluate the expression arctan(3). This gives you the value of x in radians.

6. Now, you have one value of x. To find the other value, add π radians (180°) to the initial value of x:
other value of x = (1/2) * arctan(3) + π

7. Convert the obtained values to degrees if necessary.

Thus, you should get two values for x: one from step 5 and the other from step 6.