Verify the Identity cos(x)^3sin(x)^2=(sin(x)^2-sin(x)^4)cos(x)

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Trigonometry

$\cos^{3} (x) \sin^{2} (x) = (\sin^{2} (x) - \sin^{4} (x)) \cos (x)$

Start on the right side.

$(\sin^{2} (x) - \sin^{4} (x)) \cos (x)$

Simplify the expression.

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Apply the distributive property.

$\sin^{2} (x) \cos (x) - \sin^{4} (x) \cos (x)$

Factor $\sin^{2} (x) \cos (x)$ out of $\sin^{2} (x) \cos (x) - \sin^{4} (x) \cos (x)$ .

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Factor $\sin^{2} (x) \cos (x)$ out of $\sin^{2} (x) \cos (x)$ .

$\sin^{2} (x) \cos (x) (1) - \sin^{4} (x) \cos (x)$

Factor $\sin^{2} (x) \cos (x)$ out of $- \sin^{4} (x) \cos (x)$ .

$\sin^{2} (x) \cos (x) (1) + \sin^{2} (x) \cos (x) (- \sin^{2} (x))$

Factor $\sin^{2} (x) \cos (x)$ out of $\sin^{2} (x) \cos (x) (1) + \sin^{2} (x) \cos (x) (- \sin^{2} (x))$ .

$\sin^{2} (x) \cos (x) (1 - \sin^{2} (x))$

Apply pythagorean identity.

$\sin^{2} (x) \cos (x) \cos^{2} (x)$

Multiply $\cos (x)$ by $\cos^{2} (x)$ by adding the exponents.

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Move $\cos^{2} (x)$ .

$\sin^{2} (x) (\cos^{2} (x) \cos (x))$

Multiply $\cos^{2} (x)$ by $\cos (x)$ .

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Raise $\cos (x)$ to the power of $1$ .

$\sin^{2} (x) (\cos^{2} (x) \cos^{1} (x))$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sin^{2} (x) {\cos (x)}^{2 + 1}$

Add $2$ and $1$ .

$\sin^{2} (x) \cos^{3} (x)$

Reorder the factors of $\sin^{2} (x) \cos^{3} (x)$ .

$\cos^{3} (x) \sin^{2} (x)$

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

$\cos^{3} (x) \sin^{2} (x) = (\sin^{2} (x) - \sin^{4} (x)) \cos (x)$ is an identity

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Name

Name	five hundred eighty-one million one hundred five thousand five hundred thirty-nine

Interesting facts

581105539 has 16 divisors, whose sum is 684130048
The reverse of 581105539 is 935501185
Previous prime number is 67

Basic properties

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

Name

Name	one billion five hundred fourteen million six hundred ninety-three thousand one hundred twenty-six

Interesting facts

1514693126 has 8 divisors, whose sum is 2304040464
The reverse of 1514693126 is 6213964151
Previous prime number is 71

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 38
Digital Root 2

Name

Name	one billion one hundred four million six hundred twenty-nine thousand six hundred fifty-eight

Interesting facts

1104629658 has 32 divisors, whose sum is 2415329280
The reverse of 1104629658 is 8569264011
Previous prime number is 467

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 42
Digital Root 6

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