Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Rewrite $\cot (x)$ in terms of sines and cosines.

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

Step 1.2

Multiply $\frac{\cos (x)}{\sin (x)} \cos (x)$ .

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Step 1.2.1

Combine $\frac{\cos (x)}{\sin (x)}$ and $\cos (x)$ .

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

Step 1.2.2

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

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

Step 1.2.3

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

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

Step 1.2.4

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

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

Step 1.2.5

Add $1$ and $1$ .

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

Step 1.3

Cancel the common factor of $\sin (x)$ .

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Step 1.3.1

Cancel the common factor.

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

Step 1.3.2

Rewrite the expression.

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

Step 2

Rearrange terms.

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

Step 3

Apply pythagorean identity.

$1$