Start on the left side.

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

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

Write each expression with a common denominator of <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>1</mn><mo>-</mo><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>)</mo></mrow><msup><mi>cos</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mstyle></math> , by multiplying each by an appropriate factor of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

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

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

Reorder the factors of <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>1</mn><mo>-</mo><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>)</mo></mrow><msup><mi>cos</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mstyle></math> .

Combine the numerators over the common denominator.

Simplify the numerator.

Expand <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>1</mn><mo>-</mo><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>)</mo></mrow><mrow><mo>(</mo><mn>1</mn><mo>-</mo><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>)</mo></mrow></mstyle></math> using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify and combine like terms.

Simplify each term.

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

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

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

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mrow><mo>(</mo><mo>-</mo><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>)</mo></mrow></mstyle></math> .

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

Multiply <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

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

Subtract <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mstyle></math> from <math><mstyle displaystyle="true"><mo>-</mo><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>1</mn><mo>-</mo><mn>2</mn><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>+</mo><msup><mi>sin</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>+</mo><msup><mi>cos</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mstyle></math> in a factored form.

Apply pythagorean identity.

Add <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>2</mn><mo>-</mo><mn>2</mn><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>2</mn><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>2</mn><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mo>+</mo><mn>2</mn><mrow><mo>(</mo><mo>-</mo><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>)</mo></mrow></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>1</mn><mo>-</mo><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

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

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

Do you know how to Verify the Identity (1-sin(t))/(cos(t)^2)+1/(1-sin(t))=2sec(t)^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 | sixty-four million nine hundred sixty thousand seven hundred fifty-one |
---|

- 64960751 has 4 divisors, whose sum is
**65111904** - The reverse of 64960751 is
**15706946** - Previous prime number is
**431**

- Is Prime? no
- Number parity odd
- Number length 8
- Sum of Digits 38
- Digital Root 2

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

- 1602478001 has 4 divisors, whose sum is
**1603215600** - The reverse of 1602478001 is
**1008742061** - Previous prime number is
**2179**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 29
- Digital Root 2

Name | two hundred sixty-five million ninety-three thousand nine hundred fifty-three |
---|

- 265093953 has 8 divisors, whose sum is
**353997600** - The reverse of 265093953 is
**359390562** - Previous prime number is
**659**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 42
- Digital Root 6