Start on the right side.

Apply Pythagorean identity in reverse.

Apply the distributive property.

Simplify each term.

Apply the distributive property.

Simplify each term.

Move <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> to the left of <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

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

Move <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> .

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"><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

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

Move <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn></mstyle></math> to the left of <math><mstyle displaystyle="true"><msup><mrow><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mn>3</mn></mrow></msup></mstyle></math> .

Move <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> to the left of <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

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

Subtract <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> from <math><mstyle displaystyle="true"><mn>4</mn><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Apply the sine triple-angle identity.

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

Do you know how to Verify the Identity sin(3x)=(sin(x))(4cos(x)^2-1)? 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-eight million four hundred thirty thousand one hundred ninety-seven |
---|

- 68430197 has 4 divisors, whose sum is
**74651136** - The reverse of 68430197 is
**79103486** - Previous prime number is
**11**

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

Name | three hundred eighty-two million forty-four thousand nine hundred twenty |
---|

- 382044920 has 32 divisors, whose sum is
**1547282088** - The reverse of 382044920 is
**029440283** - Previous prime number is
**5**

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

Name | one billion six hundred seventy-six million nine hundred forty-nine thousand seven hundred thirty-eight |
---|

- 1676949738 has 16 divisors, whose sum is
**3357984576** - The reverse of 1676949738 is
**8379496761** - Previous prime number is
**823**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 60
- Digital Root 6