Trigonometry Examples

$t (r + s) = r s$

Step 1

Simplify $t (r + s)$ .

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Step 1.1

Rewrite.

$0 + 0 + t (r + s) = r s$

Step 1.2

Simplify by adding zeros.

$t (r + s) = r s$

Step 1.3

Apply the distributive property.

$t r + t s = r s$

Step 2

Subtract $r s$ from both sides of the equation.

$t r + t s - r s = 0$

Step 3

Subtract $t s$ from both sides of the equation.

$t r - r s = - t s$

Step 4

Factor $r$ out of $t r - r s$ .

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Step 4.1

Factor $r$ out of $t r$ .

$r t - r s = - t s$

Step 4.2

Factor $r$ out of $- r s$ .

$r t + r (- 1 s) = - t s$

Step 4.3

Factor $r$ out of $r t + r (- 1 s)$ .

$r (t - 1 s) = - t s$

Step 5

Rewrite $- 1 s$ as $- s$ .

$r (t - s) = - t s$

Step 6

Divide each term in $r (t - s) = - t s$ by $t - s$ and simplify.

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Step 6.1

Divide each term in $r (t - s) = - t s$ by $t - s$ .

$\frac{r (t - s)}{t - s} = \frac{- t s}{t - s}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $t - s$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{r (t - s)}{t - s} = \frac{- t s}{t - s}$

Step 6.2.1.2

Divide $r$ by $1$ .

$r = \frac{- t s}{t - s}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Move the negative in front of the fraction.

$r = - \frac{t s}{t - s}$