Basic Math Examples

$\sin (A) \cdot \cos (A) \cdot \cot (A) - 1$

Step 1

Simplify terms.

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Step 1.1

Simplify each term.

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Step 1.1.1

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

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

Step 1.1.2

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

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Step 1.1.2.1

Factor $\sin (A)$ out of $\sin (A) \cos (A)$ .

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

Step 1.1.2.2

Cancel the common factor.

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

Step 1.1.2.3

Rewrite the expression.

$\cos (A) \cdot \cos (A) - 1$

Step 1.1.3

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

$\cos^{1} (A) \cdot \cos (A) - 1$

Step 1.1.4

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

$\cos^{1} (A) \cdot \cos^{1} (A) - 1$

Step 1.1.5

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

${\cos (A)}^{1 + 1} - 1$

Step 1.1.6

Add $1$ and $1$ .

$\cos^{2} (A) - 1$

Step 1.2

Simplify with factoring out.

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Step 1.2.1

Reorder $\cos^{2} (A)$ and $- 1$ .

$- 1 + \cos^{2} (A)$

Step 1.2.2

Rewrite $- 1$ as $- 1 (1)$ .

$- 1 (1) + \cos^{2} (A)$

Step 1.2.3

Factor $- 1$ out of $\cos^{2} (A)$ .

$- 1 (1) - 1 (- \cos^{2} (A))$

Step 1.2.4

Factor $- 1$ out of $- 1 (1) - 1 (- \cos^{2} (A))$ .

$- 1 (1 - \cos^{2} (A))$

Step 1.2.5

Rewrite $- 1 (1 - \cos^{2} (A))$ as $- (1 - \cos^{2} (A))$ .

$- (1 - \cos^{2} (A))$

Step 2

Apply pythagorean identity.

$- \sin^{2} (A)$