Trigonometry Examples

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

Step 1

Simplify by multiplying through.

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Step 1.1

Apply the distributive property.

$\cos (x) (4 \cos^{2} (x)) + \cos (x) \cdot - 3$

Step 1.2

Reorder.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

$4 \cos (x) \cos^{2} (x) + \cos (x) \cdot - 3$

Step 1.2.2

Move $- 3$ to the left of $\cos (x)$ .

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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Step 2.2.1

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

$4 (\cos^{2} (x) \cos^{1} (x)) - 3 \cdot \cos (x)$

Step 2.2.2

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

$4 {\cos (x)}^{2 + 1} - 3 \cdot \cos (x)$

Step 2.3

Add $2$ and $1$ .

$4 \cos^{3} (x) - 3 \cdot \cos (x)$

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

Step 3

Apply the cosine triple-angle identity.

$\cos (3 x)$