Precalculus Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Rewrite using the commutative property of multiplication.

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

Step 1.3

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

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Step 1.3.1

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

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

Step 1.3.2

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

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

Step 1.3.3

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

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

Step 1.3.4

Add $1$ and $1$ .

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

Step 1.4

Simplify each term.

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Step 1.4.1

Reorder $2 \cos (x)$ and $\sin (x)$ .

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

Step 1.4.2

Reorder $\sin (x)$ and $2$ .

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

Step 1.4.3

Apply the sine double-angle identity.

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

Step 2

Apply the cosine double-angle identity.

$\sin (2 x) + \cos (2 x)$