Calculus Examples

$\sin (u) + \cot (u) \cos (u)$

Step 1

Simplify each term.

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Step 1.1

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

$\sin (u) + \frac{\cos (u)}{\sin (u)} \cos (u)$

Step 1.2

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

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Step 1.2.1

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

$\sin (u) + \frac{\cos (u) \cos (u)}{\sin (u)}$

Step 1.2.2

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

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

Step 1.2.3

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

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

Step 1.2.4

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

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

Step 1.2.5

Add $1$ and $1$ .

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

Step 2

Simplify each term.

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Step 2.1

Factor $\cos (u)$ out of $\cos^{2} (u)$ .

$\sin (u) + \frac{\cos (u) \cos (u)}{\sin (u)}$

Step 2.2

Separate fractions.

$\sin (u) + \frac{\cos (u)}{1} \cdot \frac{\cos (u)}{\sin (u)}$

Step 2.3

Convert from $\frac{\cos (u)}{\sin (u)}$ to $\cot (u)$ .

$\sin (u) + \frac{\cos (u)}{1} \cot (u)$

Step 2.4

Divide $\cos (u)$ by $1$ .

$\sin (u) + \cos (u) \cot (u)$