# Solve for x (1-tan(x)^2)/(1+tan(x)^2)+1=2cos(x)^2

Solve for x (1-tan(x)^2)/(1+tan(x)^2)+1=2cos(x)^2
Simplify each term.
Rearrange terms.
Apply pythagorean identity.
Simplify the numerator.
Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Simplify.
Rewrite in terms of sines and cosines.
Rewrite in terms of sines and cosines.
Simplify the denominator.
Rewrite in terms of sines and cosines.
Apply the product rule to .
One to any power is one.
Multiply the numerator by the reciprocal of the denominator.
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
Simplify each term.
Multiply by .
Multiply by .
Multiply by .
Rewrite using the commutative property of multiplication.
Multiply .
Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Apply the distributive property.
Multiply by .
Cancel the common factor of .
Move the leading negative in into the numerator.
Cancel the common factor.
Rewrite the expression.
Apply the cosine double-angle identity.
Rewrite the equation as .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Take the root of both sides of the to eliminate the exponent on the left side.
The complete solution is the result of both the positive and negative portions of the solution.
Simplify the right side of the equation.
Combine the numerators over the common denominator.
Rewrite as .
Multiply by .
Combine and simplify the denominator.
Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Rewrite as .
Rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Evaluate the exponent.
Combine using the product rule for radicals.
Reorder factors in .
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the to find the first solution.
Next, use the negative value of the to find the second solution.
The complete solution is the result of both the positive and negative portions of the solution.
Set up each of the solutions to solve for .
Set up the equation to solve for .
Solve the equation for .
Since the radical is on the right side of the equation, switch the sides so it is on the left side of the equation.
Multiply both sides of the equation by .
Move to the left of .
Move all terms containing to the left side of the equation.
Subtract from both sides of the equation.
Subtract from .
Multiply each term in by
Multiply each term in by .
Multiply .
Multiply by .
Multiply by .
Multiply by .
To remove the radical on the left side of the equation, square both sides of the equation.
Simplify each side of the equation.
Simplify the left side of the equation.
Raising to any positive power yields .
Solve for .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Divide by .
Subtract from both sides of the equation.
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
The exact value of is .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
The cosine function is negative in the second and third 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.
Subtract from .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Find the period.
The period of the function can be calculated using .
Replace with in the formula for period.
Solve the equation.
The absolute value is the distance between a number and zero. The distance between and is .
Cancel the common factor of .
Cancel the common factor.
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 .
Since the radical is on the right side of the equation, switch the sides so it is on the left side of the equation.
Multiply both sides of the equation by .
Simplify both sides of the equation.
Cancel the common factor of .
Move the leading negative in into the numerator.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply.
Multiply by .
Multiply by .
Move all terms containing to the left side of the equation.
Add to both sides of the equation.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Divide by .
To remove the radical on the left side of the equation, square both sides of the equation.
Simplify each side of the equation.
Simplify the left side of the equation.
Raising to any positive power yields .
Solve for .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Divide by .
Subtract from both sides of the equation.
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
The exact value of is .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
The cosine function is negative in the second and third 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.
Subtract from .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Find the period.
The period of the function can be calculated using .
Replace with in the formula for period.
Solve the equation.
The absolute value is the distance between a number and zero. The distance between and is .
Cancel the common factor of .
Cancel the common factor.
Divide by .
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
, for any integer
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### Name

Name eighty-eight million one hundred ten thousand five hundred sixty-five

### Interesting facts

• 88110565 has 8 divisors, whose sum is 106034328
• The reverse of 88110565 is 56501188
• Previous prime number is 353

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 8
• Sum of Digits 34
• Digital Root 7

### Name

Name one hundred eighty-seven million seven hundred five thousand four hundred three

### Interesting facts

• 187705403 has 16 divisors, whose sum is 205455360
• The reverse of 187705403 is 304507781
• Previous prime number is 5279

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 35
• Digital Root 8

### Name

Name one billion nine hundred eighty-six million three hundred twenty-six thousand seven hundred seventy-four

### Interesting facts

• 1986326774 has 16 divisors, whose sum is 3036036336
• The reverse of 1986326774 is 4776236891
• Previous prime number is 397

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 53
• Digital Root 8