# Solve for x in Radians tan(x)^2=sec(x)-1

Solve for x in Radians tan(x)^2=sec(x)-1
Move all the expressions to the left side of the equation.
Subtract from both sides of the equation.
Add to both sides of the equation.
Simplify the left side of the equation.
Move .
Apply pythagorean identity.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set equal to and solve for .
Set equal to .
The range of secant is and . Since does not fall in this range, there is no solution.
No solution
No solution
Set equal to and solve for .
Set equal to .
Solve for .
Add to both sides of the equation.
Take the inverse secant of both sides of the equation to extract from inside the secant.
Simplify the right side.
The exact value of is .
The secant function is positive in the first and fourth quadrants. To find the second solution, subtract the reference angle from to find the solution in the fourth quadrant.
Subtract from .
Find the period of .
The period of the function can be calculated using .
Replace with in the formula for period.
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
, for any integer
The final solution is all the values that make true.
, for any integer
, for any integer
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### Name

Name two billion twenty-seven million nine hundred seventy-six thousand two hundred sixteen

### Interesting facts

• 2027976216 has 128 divisors, whose sum is 10711505664
• The reverse of 2027976216 is 6126797202
• Previous prime number is 37

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 42
• Digital Root 6

### Name

Name three hundred fifteen million three hundred two thousand eight hundred twenty-seven

### Interesting facts

• 315302827 has 8 divisors, whose sum is 360466400
• The reverse of 315302827 is 728203513
• Previous prime number is 4129

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 31
• Digital Root 4

### Name

Name one hundred forty-six million nine hundred nineteen thousand fifty

### Interesting facts

• 146919050 has 16 divisors, whose sum is 317345256
• The reverse of 146919050 is 050919641
• Previous prime number is 5

### Basic properties

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