Trigonometry Examples

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

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

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)

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

Step 1.1.2

Reorder

sin (x)

$\sin (x)$ and

cot (x)

$\cot (x)$ .

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

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

Step 1.1.3

Rewrite

2 sin (x) cot (x)

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

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

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

Step 1.1.4

Cancel the common factors.

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

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

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

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

Step 1.2

Rewrite

cot (x)

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

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

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

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

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

Step 2

Convert from

\frac{cos (x)}{sin (x)}

$\frac{\cos (x)}{\sin (x)}$ to

cot (x)

$\cot (x)$ .

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

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