Algebra Examples

$(\sec (30 °)) (\cos (30 °)) - (\tan (60 °)) \cot (60 °)$

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

Rewrite $(\sec (30 °)) (\cos (30 °))$ in terms of sines and cosines.

$\frac{1}{\cos (30 °)} \cos (30 °) - (\tan (60 °)) \cot (60 °)$

Step 1.1.2

Cancel the common factors.

$1 - (\tan (60 °)) \cot (60 °)$

Step 1.2

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

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Step 1.2.1

Move parentheses.

$1 - (\tan (60 °) \cot (60 °))$

Step 1.2.2

Reorder $\tan (60 °)$ and $\cot (60 °)$ .

$1 - (\cot (60 °) \tan (60 °))$

Step 1.2.3

Rewrite $- (\tan (60 °)) \cot (60 °)$ in terms of sines and cosines.

$1 - (\frac{\cos (60 °)}{\sin (60 °)} \cdot \frac{\sin (60 °)}{\cos (60 °)})$

Step 1.2.4

Cancel the common factors.

$1 - 1 \cdot 1$

Step 1.3

Multiply $- 1$ by $1$ .

$1 - 1$

Step 2

Subtract $1$ from $1$ .

$0$