Simplify the expression.

Rewrite <math><mstyle displaystyle="true"><msup><mi>sec</mi><mrow><mn>4</mn></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mi>sec</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msup><mi>tan</mi><mrow><mn>4</mn></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mi>tan</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Since both terms are perfect squares, factor using the difference of squares formula, <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><msup><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mrow><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo></mrow><mrow><mo>(</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo>)</mo></mrow></mstyle></math> where <math><mstyle displaystyle="true"><mi>a</mi><mo>=</mo><msup><mi>sec</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> and <math><mstyle displaystyle="true"><mi>b</mi><mo>=</mo><msup><mi>tan</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Apply pythagorean identity.

Multiply <math><mstyle displaystyle="true"><msup><mi>sec</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>+</mo><msup><mi>tan</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><msup><mi>tan</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> from both sides of the equation.

Subtract <math><mstyle displaystyle="true"><msup><mi>tan</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> from <math><mstyle displaystyle="true"><mn>2</mn><msup><mi>tan</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Take the <math><mstyle displaystyle="true"><mtext class="not-bold-word">square</mtext></mstyle></math> root of both sides of the <math><mstyle displaystyle="true"><mtext class="not-bold-word">equation</mtext></mstyle></math> to eliminate the exponent on the left side.

First, use the positive value of the <math><mstyle displaystyle="true"><mo>±</mo></mstyle></math> to find the first solution.

Next, use the negative value of the <math><mstyle displaystyle="true"><mo>±</mo></mstyle></math> 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 <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Set up the equation to solve for <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Since the radical is on the right side of the equation, switch the sides so it is on the left side of the equation.

To remove the radical on the left side of the equation, square both sides of the equation.

Simplify the left side of the equation.

Solve for <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Replace the <math><mstyle displaystyle="true"><msup><mi>tan</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> with <math><mstyle displaystyle="true"><msup><mi>sec</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>-</mo><mn>1</mn></mstyle></math> based on the <math><mstyle displaystyle="true"><msup><mi>tan</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>+</mo><mn>1</mn><mo>=</mo><msup><mi>sec</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> identity.

Combine the opposite terms in <math><mstyle displaystyle="true"><mn>1</mn><mo>+</mo><msup><mi>sec</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>-</mo><mn>1</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><msup><mi>sec</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> and <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

For the two functions to be equal, the arguments of each must be equal.

Move all terms containing <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> to the left side of the equation.

Subtract <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> from both sides of the equation.

Subtract <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> from <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Since <math><mstyle displaystyle="true"><mn>0</mn><mo>=</mo><mn>0</mn></mstyle></math> , the equation will always be true.

All real numbers

All real numbers

All real numbers

Set up the equation to solve for <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Since the radical is on the right side of the equation, switch the sides so it is on the left side of the equation.

To remove the radical on the left side of the equation, square both sides of the equation.

Simplify the left side of the equation.

Solve for <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Simplify the left side.

Rearrange terms.

Apply pythagorean identity.

Simplify the expression.

Raise <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><msup><mi>sec</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

For the two functions to be equal, the arguments of each must be equal.

Move all terms containing <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> to the left side of the equation.

Subtract <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> from both sides of the equation.

Subtract <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> from <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Since <math><mstyle displaystyle="true"><mn>0</mn><mo>=</mo><mn>0</mn></mstyle></math> , the equation will always be true.

All real numbers

All real numbers

All real numbers

The complete solution is the set of all solutions.

No solution

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Name | two hundred eighty-two million two hundred seventeen thousand three hundred two |
---|

- 282217302 has 16 divisors, whose sum is
**752579520** - The reverse of 282217302 is
**203712282** - Previous prime number is
**3**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 27
- Digital Root 9

Name | four hundred eighteen million twenty-seven thousand three hundred forty-three |
---|

- 418027343 has 8 divisors, whose sum is
**434374656** - The reverse of 418027343 is
**343720814** - Previous prime number is
**151**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 32
- Digital Root 5

Name | one billion five hundred forty-eight million seventy-five thousand seven hundred seventy-five |
---|

- 1548075775 has 8 divisors, whose sum is
**2229229152** - The reverse of 1548075775 is
**5775708451** - Previous prime number is
**5**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 49
- Digital Root 4