Trigonometry Examples

$\cos (x) (2 \cos (x) - 1)$

Step 1

Simplify by multiplying through.

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Step 1.1

Apply the distributive property.

$\cos (x) (2 \cos (x)) + \cos (x) \cdot - 1$

Step 1.2

Reorder.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

$2 \cos (x) \cos (x) + \cos (x) \cdot - 1$

Step 1.2.2

Move $- 1$ to the left of $\cos (x)$ .

$2 \cos (x) \cos (x) - 1 \cdot \cos (x)$

Step 2

Simplify each term.

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Step 2.1

Multiply $2 \cos (x) \cos (x)$ .

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Step 2.1.1

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

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

Step 2.1.2

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

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

Step 2.1.3

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

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

Step 2.1.4

Add $1$ and $1$ .

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

Step 2.2

Rewrite $- 1 \cos (x)$ as $- \cos (x)$ .

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