Add <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> to both sides of the equation.

Divide each term in <math><mstyle displaystyle="true"><mn>16</mn><msup><mi>sec</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>=</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> .

Simplify the left side.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> .

Cancel the common factor.

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

Take the square root of both sides of the equation to eliminate the exponent on the left side.

Rewrite <math><mstyle displaystyle="true"><msqrt><mfrac><mrow><mn>1</mn></mrow><mrow><mn>16</mn></mrow></mfrac></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>1</mn></msqrt></mrow><mrow><msqrt><mn>16</mn></msqrt></mrow></mfrac></mstyle></math> .

Any root of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> is <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Simplify the denominator.

Rewrite <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>4</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical, assuming positive real numbers.

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>θ</mi></mstyle></math> .

The range of secant is <math><mstyle displaystyle="true"><mi>y</mi><mo>≤</mo><mo>-</mo><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mi>y</mi><mo>≥</mo><mn>1</mn></mstyle></math> . Since <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> does not fall in this range, there is no solution.

No solution

No solution

The range of secant is <math><mstyle displaystyle="true"><mi>y</mi><mo>≤</mo><mo>-</mo><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mi>y</mi><mo>≥</mo><mn>1</mn></mstyle></math> . Since <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> does not fall in this range, there is no solution.

No solution

No solution

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Name | six hundred ninety-eight million eighty thousand seven hundred eighty-four |
---|

- 698080784 has 32 divisors, whose sum is
**3534034050** - The reverse of 698080784 is
**487080896** - Previous prime number is
**2**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 50
- Digital Root 5

Name | seven hundred one million eight hundred seventy thousand |
---|

- 701870000 has 128 divisors, whose sum is
**4267274400** - The reverse of 701870000 is
**000078107** - Previous prime number is
**1625**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 23
- Digital Root 5

Name | one billion four hundred seventy million four hundred thirty-six thousand eight hundred eighty-four |
---|

- 1470436884 has 128 divisors, whose sum is
**5487390720** - The reverse of 1470436884 is
**4886340741** - Previous prime number is
**7**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 45
- Digital Root 9