Simplify (sin(theta)-cos(theta))^2

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Trigonometry

${(\sin (θ) - \cos (θ))}^{2}$

Rewrite ${(\sin (θ) - \cos (θ))}^{2}$ as $(\sin (θ) - \cos (θ)) (\sin (θ) - \cos (θ))$ .

$(\sin (θ) - \cos (θ)) (\sin (θ) - \cos (θ))$

Expand $(\sin (θ) - \cos (θ)) (\sin (θ) - \cos (θ))$ using the FOIL Method.

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Apply the distributive property.

$\sin (θ) (\sin (θ) - \cos (θ)) - \cos (θ) (\sin (θ) - \cos (θ))$

Apply the distributive property.

$\sin (θ) \sin (θ) + \sin (θ) (- \cos (θ)) - \cos (θ) (\sin (θ) - \cos (θ))$

Apply the distributive property.

$\sin (θ) \sin (θ) + \sin (θ) (- \cos (θ)) - \cos (θ) \sin (θ) - \cos (θ) (- \cos (θ))$

Simplify and combine like terms.

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Simplify each term.

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Multiply $\sin (θ) \sin (θ)$ .

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Raise $\sin (θ)$ to the power of $1$ .

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

Raise $\sin (θ)$ to the power of $1$ .

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

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

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

Add $1$ and $1$ .

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

Rewrite using the commutative property of multiplication.

$\sin^{2} (θ) - \sin (θ) \cos (θ) - \cos (θ) \sin (θ) - \cos (θ) (- \cos (θ))$

Multiply $- \cos (θ) (- \cos (θ))$ .

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Multiply $- 1$ by $- 1$ .

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

Multiply $\cos (θ)$ by $1$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

Reorder the factors of $- \sin (θ) \cos (θ)$ .

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

Subtract $\cos (θ) \sin (θ)$ from $- \cos (θ) \sin (θ)$ .

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

Move $\cos^{2} (θ)$ .

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

Apply pythagorean identity.

$1 - 2 \cos (θ) \sin (θ)$

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Name

Name	one billion seventy-six million one hundred fourteen thousand seven hundred fifty

Interesting facts

1076114750 has 32 divisors, whose sum is 2016806688
The reverse of 1076114750 is 0574116701
Previous prime number is 1123

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 32
Digital Root 5

Name

Name	three hundred fifty-seven million six hundred fifty thousand one hundred seventy-four

Interesting facts

357650174 has 32 divisors, whose sum is 621637632
The reverse of 357650174 is 471056753
Previous prime number is 191

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 38
Digital Root 2

Name

Name	one billion four hundred fifty-three million six hundred thirty-seven thousand one hundred thirty

Interesting facts

1453637130 has 64 divisors, whose sum is 2894476032
The reverse of 1453637130 is 0317363541
Previous prime number is 11

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 33
Digital Root 6

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