Finite Math Examples

$\frac{\sin (π - a) \cdot \cos (\frac{3 π}{2} - a) \cdot (c t g (\frac{π}{2} + a))}{t g (2 π - a)}$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Cancel the common factor of $t$ .

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Step 1.1.1

Cancel the common factor.

$\frac{\sin (π - a) \cdot \cos (\frac{3 π}{2} - a) \cdot (c t g (\frac{π}{2} + a))}{t g (2 π - a)}$

Step 1.1.2

Rewrite the expression.

$\frac{\sin (π - a) \cdot \cos (\frac{3 π}{2} - a) \cdot (c g (\frac{π}{2} + a))}{g (2 π - a)}$

Step 1.2

Cancel the common factor of $g$ .

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Step 1.2.1

Cancel the common factor.

$\frac{\sin (π - a) \cdot \cos (\frac{3 π}{2} - a) \cdot (c g (\frac{π}{2} + a))}{g (2 π - a)}$

Step 1.2.2

Rewrite the expression.

$\frac{\sin (π - a) \cdot \cos (\frac{3 π}{2} - a) \cdot (c (\frac{π}{2} + a))}{2 π - a}$

Step 2

Simplify the numerator.

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Step 2.1

Remove unnecessary parentheses.

$\frac{\sin (π - a) \cdot \cos (\frac{3 π}{2} - a) c (\frac{π}{2} + a)}{2 π - a}$

Step 2.2

To write $a$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\sin (π - a) \cdot \cos (\frac{3 π}{2} - a) c (\frac{π}{2} + a \cdot \frac{2}{2})}{2 π - a}$

Step 2.3

Combine $a$ and $\frac{2}{2}$ .

$\frac{\sin (π - a) \cdot \cos (\frac{3 π}{2} - a) c (\frac{π}{2} + \frac{a \cdot 2}{2})}{2 π - a}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{\sin (π - a) \cdot \cos (\frac{3 π}{2} - a) c \frac{π + a \cdot 2}{2}}{2 π - a}$

Step 2.5

Move $2$ to the left of $a$ .

$\frac{\sin (π - a) \cdot \cos (\frac{3 π}{2} - a) c \frac{π + 2 a}{2}}{2 π - a}$

Step 3

Simplify the numerator.

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Step 3.1

Combine $\sin (π - a)$ and $\frac{π + 2 a}{2}$ .

$\frac{\cos (\frac{3 π}{2} - a) c \frac{\sin (π - a) (π + 2 a)}{2}}{2 π - a}$

Step 3.2

Combine $\cos (\frac{3 π}{2} - a)$ and $\frac{\sin (π - a) (π + 2 a)}{2}$ .

$\frac{c \frac{\cos (\frac{3 π}{2} - a) (\sin (π - a) (π + 2 a))}{2}}{2 π - a}$

Step 3.3

Combine $c$ and $\frac{\cos (\frac{3 π}{2} - a) (\sin (π - a) (π + 2 a))}{2}$ .

$\frac{\frac{c (\cos (\frac{3 π}{2} - a) (\sin (π - a) (π + 2 a)))}{2}}{2 π - a}$

Step 4

Remove parentheses.

$\frac{\frac{c \cos (\frac{3 π}{2} - a) \sin (π - a) (π + 2 a)}{2}}{2 π - a}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$\frac{c \cos (\frac{3 π}{2} - a) \sin (π - a) (π + 2 a)}{2} \cdot \frac{1}{2 π - a}$

Step 6

Multiply $\frac{c \cos (\frac{3 π}{2} - a) \sin (π - a) (π + 2 a)}{2}$ by $\frac{1}{2 π - a}$ .

$\frac{c \cos (\frac{3 π}{2} - a) \sin (π - a) (π + 2 a)}{2 (2 π - a)}$