Finite Math Examples

$\frac{\cos (a)}{\sin (a) \cot (a)} = 1$

Step 1

Divide each term in the equation by $\cos (a)$ .

$\frac{\frac{\cos (a)}{\sin (a) \cot (a)}}{\cos (a)} = \frac{1}{\cos (a)}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{\cos (a)}{\sin (a) \cot (a)} \cdot \frac{1}{\cos (a)} = \frac{1}{\cos (a)}$

Step 3

Cancel the common factor of $\cos (a)$ .

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Step 3.1

Cancel the common factor.

$\frac{\cos (a)}{\sin (a) \cot (a)} \cdot \frac{1}{\cos (a)} = \frac{1}{\cos (a)}$

Step 3.2

Rewrite the expression.

$\frac{1}{\sin (a) \cot (a)} = \frac{1}{\cos (a)}$

Step 4

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

$\frac{1}{\sin (a) (\frac{\cos (a)}{\sin (a)})} = \frac{1}{\cos (a)}$

Step 5

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

$\frac{1}{\frac{\sin (a) \cos (a)}{\sin (a)}} = \frac{1}{\cos (a)}$

Step 6

Reduce the expression by cancelling the common factors.

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Step 6.1

Reduce the expression $\frac{\sin (a) \cos (a)}{\sin (a)}$ by cancelling the common factors.

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Step 6.1.1

Cancel the common factor.

$\frac{1}{\frac{\sin (a) \cos (a)}{\sin (a)}} = \frac{1}{\cos (a)}$

Step 6.1.2

Rewrite the expression.

$\frac{1}{\frac{\cos (a)}{1}} = \frac{1}{\cos (a)}$

Step 6.2

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

$\frac{1}{\cos (a)} = \frac{1}{\cos (a)}$

Step 7

Convert from $\frac{1}{\cos (a)}$ to $\sec (a)$ .

$\sec (a) = \frac{1}{\cos (a)}$

Step 8

Convert from $\frac{1}{\cos (a)}$ to $\sec (a)$ .

$\sec (a) = \sec (a)$

Step 9

For the two functions to be equal, the arguments of each must be equal.

$a = a$

Step 10

Move all terms containing $a$ to the left side of the equation.

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Step 10.1

Subtract $a$ from both sides of the equation.

$a - a = 0$

Step 10.2

Subtract $a$ from $a$ .

$0 = 0$

Step 11

Since $0 = 0$ , the equation will always be true.

Always true