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irga5000 [103]
3 years ago
10

You buy the same number of brushes,rollers,and paint cans. Write an expression in simplest form that represents the total amount

of money you spend for painting supplies
Mathematics
1 answer:
bearhunter [10]3 years ago
7 0
BrushesX+ rollersX+ paint cansX= total
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1-sina/cosa=cosa/2-sina/2÷cosa/2+sina/2​
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Step-by-step explanation:

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we've,

<h3>(<u>Cosa</u><u>/</u><u>2</u><u> </u><u>-</u><u> </u><u>sina</u><u>/</u><u>2</u><u>)</u></h3><h3>(<u>Cosa/</u><u>2</u><u> </u><u>+</u><u> </u><u>sina</u><u>/</u><u>2</u><u>)</u></h3>

Let's Rationalise the Denominator.

we get,

<h3>(<u>Cosa/</u><u>2</u><u> </u><u>-</u><u> </u><u>sina</u><u>/</u><u>2</u><u>)</u><u>^</u><u>2</u></h3><h3><u>(</u><u>cosa</u><u>/</u><u>2</u><u>)</u><u>^</u><u>2</u><u> </u><u>-</u><u> </u><u>(</u><u>sina</u><u>/</u><u>2</u><u>)</u><u>^</u><u>2</u></h3>

The numerator is in form of (a-b)^2 and the denominator is in form of a^2-b^2. Now,

By formula,

<h3>(<u>Cosa/</u><u>2</u><u>)</u><u>^</u><u>2</u><u> </u><u>-2cosa</u><u>/</u><u>2</u><u>.</u><u>s</u><u>i</u><u>n</u><u>a</u><u>/</u><u>2</u><u> </u><u>+</u><u> </u><u>(</u><u>sina</u><u>/</u><u>2</u><u>)</u><u>^</u><u>2</u> </h3><h3> cosa</h3>

Here I substituted Cosa in place of (Cosa/2)^2 - (sina/2)^2 because it's the formula of cosa in sub multiple angle form.

<h3>In the numerator, </h3>

(sina/2)^2 + (Cosa/2)^2 =1.........( by formula)

so we have,

<h3><u>1</u><u> </u><u>-</u><u> </u><u>2</u><u>s</u><u>i</u><u>n</u><u>a</u><u>/</u><u>2</u><u>.</u><u>c</u><u>o</u><u>s</u><u>a</u><u>/</u><u>2</u></h3><h3>Cosa</h3>

<h3 /><h3 /><h3><u>1</u><u> </u><u>-</u><u> </u><u>sina</u> {because 2sina/2.cosa/2=sina)</h3><h3>Cosa</h3>

LHS proved.

Thank You.

5 0
3 years ago
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