Start on the right side.

Factor <math><mstyle displaystyle="true"><msup><mi>cot</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> out of <math><mstyle displaystyle="true"><msup><mi>cot</mi><mrow><mn>4</mn></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Multiply by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><msup><mi>cot</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> out of <math><mstyle displaystyle="true"><msup><mi>cot</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><msup><mi>cot</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>+</mo><msup><mi>cot</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>⋅</mo><mn>1</mn></mstyle></math> .

Rearrange terms.

Apply pythagorean identity.

Apply Pythagorean identity in reverse.

Apply the reciprocal identity to <math><mstyle displaystyle="true"><mi>csc</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Apply the reciprocal identity to <math><mstyle displaystyle="true"><mi>csc</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Apply the product rule to <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> .

Apply the product rule to <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> .

One to any power is one.

One to any power is one.

Apply the distributive property.

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

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

Multiply <math><mstyle displaystyle="true"><msup><mrow><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> by <math><mstyle displaystyle="true"><msup><mrow><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> by adding the exponents.

Use the power rule <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><msup><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mo>+</mo><mi>n</mi></mrow></msup></mstyle></math> to combine exponents.

Add <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn><mfrac><mrow><mn>1</mn></mrow><mrow><msup><mrow><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></mstyle></math> as <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>1</mn></mrow><mrow><msup><mrow><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></mstyle></math> .

To write <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>1</mn></mrow><mrow><msup><mrow><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></mstyle></math> as a fraction with a common denominator, multiply by <math><mstyle displaystyle="true"><mfrac><mrow><msup><mrow><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><msup><mrow><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></mstyle></math> .

Write each expression with a common denominator of <math><mstyle displaystyle="true"><msup><mrow><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mn>4</mn></mrow></msup></mstyle></math> , by multiplying each by an appropriate factor of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Combine.

Multiply <math><mstyle displaystyle="true"><msup><mrow><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> by <math><mstyle displaystyle="true"><msup><mrow><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> by adding the exponents.

Use the power rule <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><msup><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mo>+</mo><mi>n</mi></mrow></msup></mstyle></math> to combine exponents.

Add <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Combine the numerators over the common denominator.

Simplify the numerator.

Now consider the left side of the equation.

Apply the reciprocal identity to <math><mstyle displaystyle="true"><mi>csc</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Apply the product rule to <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> .

Simplify each term.

One to any power is one.

One to any power is one.

To write <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>1</mn></mrow><mrow><msup><mrow><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></mstyle></math> as a fraction with a common denominator, multiply by <math><mstyle displaystyle="true"><mfrac><mrow><msup><mrow><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><msup><mrow><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></mstyle></math> .

Write each expression with a common denominator of <math><mstyle displaystyle="true"><msup><mrow><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mn>4</mn></mrow></msup></mstyle></math> , by multiplying each by an appropriate factor of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Combine.

Multiply <math><mstyle displaystyle="true"><msup><mrow><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> by <math><mstyle displaystyle="true"><msup><mrow><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> by adding the exponents.

Use the power rule <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><msup><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mo>+</mo><mi>n</mi></mrow></msup></mstyle></math> to combine exponents.

Add <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Combine the numerators over the common denominator.

Simplify the numerator.

Because the two sides have been shown to be equivalent, the equation is an identity.

Do you know how to Verify the Identity csc(x)^4-csc(x)^2=cot(x)^4+cot(x)^2? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Name | four hundred ninety-nine million five hundred twenty-seven thousand two hundred forty-five |
---|

- 499527245 has 32 divisors, whose sum is
**699217920** - The reverse of 499527245 is
**542725994** - Previous prime number is
**179**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 47
- Digital Root 2

Name | five hundred seventy-four million four hundred twenty-six thousand four hundred thirty-two |
---|

- 574426432 has 512 divisors, whose sum is
**6811630200** - The reverse of 574426432 is
**234624475** - Previous prime number is
**173**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 37
- Digital Root 1

Name | one billion five hundred nine million five hundred eleven thousand three hundred forty-six |
---|

- 1509511346 has 16 divisors, whose sum is
**2957410176** - The reverse of 1509511346 is
**6431159051** - Previous prime number is
**7**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 35
- Digital Root 8