Find Where Undefined/Discontinuous (-1+cot(w)^2+cos(w)^2tan(w)^2)/(csc(w)^2)=cos(w)^4

Move <math><mstyle displaystyle="true"><msup><mi>cos</mi><mrow><mn>4</mn></mrow></msup><mrow><mo>(</mo><mi>w</mi><mo>)</mo></mrow></mstyle></math> to the left side of the equation by subtracting it from both sides.

Set the denominator in <math><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><mn>1</mn><mo>+</mo><msup><mi>cot</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>w</mi><mo>)</mo></mrow><mo>+</mo><msup><mi>cos</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>w</mi><mo>)</mo></mrow><msup><mi>tan</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>w</mi><mo>)</mo></mrow></mrow><mrow><msup><mi>csc</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>w</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> to find where the expression is undefined.

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.

The complete solution is the result of both the positive and negative portions of the solution.

Simplify the right side of the equation.

Rewrite <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>0</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

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

The range of cosecant 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"><mn>0</mn></mstyle></math> does not fall in this range, there is no solution.

No solution

No solution

Set the argument in <math><mstyle displaystyle="true"><mi>cot</mi><mrow><mo>(</mo><mi>w</mi><mo>)</mo></mrow></mstyle></math> equal to <math><mstyle displaystyle="true"><mi>π</mi><mi>n</mi></mstyle></math> to find where the expression is undefined.

Set the argument in <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mi>w</mi><mo>)</mo></mrow></mstyle></math> equal to <math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>+</mo><mi>π</mi><mi>n</mi></mstyle></math> to find where the expression is undefined.

The equation is undefined where the denominator equals <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> , the argument of a square root is less than <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> , or the argument of a logarithm is less than or equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Set-Builder Notation:

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Name | one billion six hundred one million two hundred twelve thousand five hundred eighteen |
---|

- 1601212518 has 64 divisors, whose sum is
**2838326400** - The reverse of 1601212518 is
**8152121061** - Previous prime number is
**37**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 27
- Digital Root 9

Name | one billion one hundred seventy-seven million nine hundred ninety-two thousand nine hundred twenty-five |
---|

- 1177992925 has 16 divisors, whose sum is
**1698091776** - The reverse of 1177992925 is
**5292997711** - Previous prime number is
**971**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 52
- Digital Root 7

Name | one billion eight hundred eighty-seven million sixteen thousand five hundred fifty-two |
---|

- 1887016552 has 16 divisors, whose sum is
**6368680890** - The reverse of 1887016552 is
**2556107881** - Previous prime number is
**2**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 43
- Digital Root 7