Trigonometry Examples

$R (b + c) = a \sqrt{b c}$

Step 1

Rewrite the equation as $a \sqrt{b c} = R (b + c)$ .

$a \sqrt{b c} = R (b + c)$

Step 2

Divide each term in $a \sqrt{b c} = R (b + c)$ by $\sqrt{b c}$ and simplify.

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Step 2.1

Divide each term in $a \sqrt{b c} = R (b + c)$ by $\sqrt{b c}$ .

$\frac{a \sqrt{b c}}{\sqrt{b c}} = \frac{R (b + c)}{\sqrt{b c}}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $\sqrt{b c}$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{a \sqrt{b c}}{\sqrt{b c}} = \frac{R (b + c)}{\sqrt{b c}}$

Step 2.2.1.2

Divide $a$ by $1$ .

$a = \frac{R (b + c)}{\sqrt{b c}}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply $\frac{R (b + c)}{\sqrt{b c}}$ by $\frac{\sqrt{b c}}{\sqrt{b c}}$ .

$a = \frac{R (b + c)}{\sqrt{b c}} \cdot \frac{\sqrt{b c}}{\sqrt{b c}}$

Step 2.3.2

Combine and simplify the denominator.

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Step 2.3.2.1

Multiply $\frac{R (b + c)}{\sqrt{b c}}$ by $\frac{\sqrt{b c}}{\sqrt{b c}}$ .

$a = \frac{R (b + c) \sqrt{b c}}{\sqrt{b c} \sqrt{b c}}$

Step 2.3.2.2

Raise $\sqrt{b c}$ to the power of $1$ .

$a = \frac{R (b + c) \sqrt{b c}}{{\sqrt{b c}}^{1} \sqrt{b c}}$

Step 2.3.2.3

Raise $\sqrt{b c}$ to the power of $1$ .

$a = \frac{R (b + c) \sqrt{b c}}{{\sqrt{b c}}^{1} {\sqrt{b c}}^{1}}$

Step 2.3.2.4

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

$a = \frac{R (b + c) \sqrt{b c}}{{\sqrt{b c}}^{1 + 1}}$

Step 2.3.2.5

Add $1$ and $1$ .

$a = \frac{R (b + c) \sqrt{b c}}{{\sqrt{b c}}^{2}}$

Step 2.3.2.6

Rewrite ${\sqrt{b c}}^{2}$ as $b c$ .

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Step 2.3.2.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{b c}$ as ${(b c)}^{\frac{1}{2}}$ .

$a = \frac{R (b + c) \sqrt{b c}}{{({(b c)}^{\frac{1}{2}})}^{2}}$

Step 2.3.2.6.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$a = \frac{R (b + c) \sqrt{b c}}{{(b c)}^{\frac{1}{2} \cdot 2}}$

Step 2.3.2.6.3

Combine $\frac{1}{2}$ and $2$ .

$a = \frac{R (b + c) \sqrt{b c}}{{(b c)}^{\frac{2}{2}}}$

Step 2.3.2.6.4

Cancel the common factor of $2$ .

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Step 2.3.2.6.4.1

Cancel the common factor.

$a = \frac{R (b + c) \sqrt{b c}}{{(b c)}^{\frac{2}{2}}}$

Step 2.3.2.6.4.2

Rewrite the expression.

$a = \frac{R (b + c) \sqrt{b c}}{{(b c)}^{1}}$

Step 2.3.2.6.5

Simplify.

$a = \frac{R (b + c) \sqrt{b c}}{b c}$

Step 2.3.3

Reorder factors in $\frac{R (b + c) \sqrt{b c}}{b c}$ .

$a = \frac{R \sqrt{b c} (b + c)}{b c}$