Trigonometry Examples

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

Step 1

Simplify each term.

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Step 1.1

Rewrite in terms of sines and cosines, then cancel the common factors.

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Step 1.1.1

Add parentheses.

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

Step 1.1.2

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

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

Step 1.1.3

Rewrite $2 \sin (x) \cot (x)$ in terms of sines and cosines.

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

Step 1.1.4

Cancel the common factors.

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

Step 1.2

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

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

Step 2

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

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