Solve for x 2tan(x)=1-tan(x)^2

Math
Substitute for .
Add to both sides of the equation.
Move to the left side of the equation by subtracting it from both sides.
Use the quadratic formula to find the solutions.
Substitute the values , , and into the quadratic formula and solve for .
Simplify.
Tap for more steps…
Simplify the numerator.
Tap for more steps…
Raise to the power of .
Multiply by .
Multiply by .
Add and .
Rewrite as .
Tap for more steps…
Factor out of .
Rewrite as .
Pull terms out from under the radical.
Multiply by .
Simplify .
The final answer is the combination of both solutions.
Substitute for .
Set up each of the solutions to solve for .
Set up the equation to solve for .
Solve the equation for .
Tap for more steps…
Convert the right side of the equation to its decimal equivalent.
Take the inverse tangent of both sides of the equation to extract from inside the tangent.
Evaluate .
The tangent function is positive in the first and third quadrants. To find the second solution, add the reference angle from to find the solution in the fourth quadrant.
Simplify .
Tap for more steps…
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Tap for more steps…
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Tap for more steps…
Move to the left of .
Add and .
Find the period.
Tap for more steps…
The period of the function can be calculated using .
Replace with in the formula for period.
Solve the equation.
Tap for more steps…
The absolute value is the distance between a number and zero. The distance between and is .
Divide by .
The period of the function is so values will repeat every radians in both directions.
, for any integer
, for any integer
Set up the equation to solve for .
Solve the equation for .
Tap for more steps…
Convert the right side of the equation to its decimal equivalent.
Take the inverse tangent of both sides of the equation to extract from inside the tangent.
Evaluate .
The tangent function is negative in the second and fourth quadrants. To find the second solution, subtract the reference angle from to find the solution in the third quadrant.
Simplify the expression to find the second solution.
Tap for more steps…
Simplify .
Tap for more steps…
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Tap for more steps…
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Tap for more steps…
Multiply by .
Subtract from .
Move the negative in front of the fraction.
Add to .
The resulting angle of is positive and coterminal with .
Find the period.
Tap for more steps…
The period of the function can be calculated using .
Replace with in the formula for period.
Solve the equation.
Tap for more steps…
The absolute value is the distance between a number and zero. The distance between and is .
Divide by .
Add to every negative angle to get positive angles.
Tap for more steps…
Add to to find the positive angle.
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Tap for more steps…
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Tap for more steps…
Move to the left of .
Subtract from .
List the new angles.
The period of the function is so values will repeat every radians in both directions.
, for any integer
, for any integer
List all of the results found in the previous steps.
, for any integer
The complete solution is the set of all solutions.
, for any integer
Consolidate the answers.
, for any integer
Solve for x 2tan(x)=1-tan(x)^2

Download our
App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Scroll to top