Trigonometry Examples

$\cos (2 x) \cos (x)$

Step 1

Use the double-angle identity to transform $\cos (2 x)$ to $2 \cos^{2} (x) - 1$ .

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

Step 2

Apply the distributive property.

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

Step 3

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

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Step 3.1

Move $\cos (x)$ .

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

Step 3.2

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

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Step 3.2.1

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

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

Step 3.2.2

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

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

Step 3.3

Add $1$ and $2$ .

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

Step 4

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

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