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Hoochie [10]
2 years ago
11

Cot^2x/cscx-1=1+sinx/sinx

Mathematics
1 answer:
KATRIN_1 [288]2 years ago
5 0
\bf \textit{difference of squares}
\\\\
(a-b)(a+b) = a^2-b^2\qquad \qquad 
a^2-b^2 = (a-b)(a+b)
\\\\\\
sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta)\\\\
-------------------------------\\\\
\cfrac{cot^2(x)}{csc(x)-1}=\cfrac{1+sin(x)}{sin(x)}\impliedby \textit{let's do the left-hand-side}

\bf \cfrac{\quad \frac{cos^2(x)}{sin^2(x)}\quad }{\frac{1}{sin(x)}-1}\implies \cfrac{\quad \frac{cos^2(x)}{sin^2(x)}\quad }{\frac{1-sin(x)}{sin(x)}}\implies \cfrac{cos^2(x)}{sin^2(x)}\cdot \cfrac{sin(x)}{1-sin(x)}
\\\\\\
\cfrac{cos^2(x)}{sin(x)}\cdot \cfrac{1}{1-sin(x)}\implies \cfrac{cos^2(x)}{sin(x)[1-sin(x)]}

\bf \cfrac{1-sin^2(x)}{sin(x)[1-sin(x)]}\implies \cfrac{1^2-sin^2(x)}{sin(x)[1-sin(x)]}
\\\\\\
\cfrac{\underline{[1-sin(x)]}~[1+sin(x)]}{sin(x)\underline{[1-sin(x)]}}\implies \cfrac{1+sin(x)}{sin(x)}
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Please help me with this.
tatyana61 [14]

By understanding and applying the characteristics of <em>piecewise</em> functions, the results are listed below:

  1. r (- 3) = 15
  2. r (- 1) = 11
  3. r (1) = - 7
  4. r (5) = 13

<h3>How to evaluate a piecewise function at given values</h3>

In this question we have a <em>piecewise</em> function formed by three expressions associated with three respective intervals. We need to evaluate the expression at a value of the <em>respective</em> interval:

<h3>r(- 3): </h3>

-3 ∈ (- ∞, -1]

r(- 3) = - 2 · (- 3) + 9

r (- 3) = 15

<h3>r(- 1):</h3>

-1 ∈ (- ∞, -1]

r(- 1) = - 2 · (- 1) + 9

r (- 1) = 11

<h3>r(1):</h3>

1 ∈ (-1, 5)

r(1) = 2 · 1² - 4 · 1 - 5

r (1) = - 7

<h3>r(5):</h3>

5 ∈ [5, + ∞)

r(5) = 4 · 5 - 7

r (5) = 13

By understanding and applying the characteristics of <em>piecewise</em> functions, the results are listed below:

  1. r (- 3) = 15
  2. r (- 1) = 11
  3. r (1) = - 7
  4. r (5) = 13

To learn more on piecewise functions: brainly.com/question/12561612

#SPJ1

7 0
1 year ago
Y = x - 4<br><br> y = 4x + 2<br><br> x =<br> y =
marshall27 [118]

Answer:

x=-2 y=-6

Step-by-step explanation:

x-4=4x+2

subtract x from both sides

-4=3x+2

subtract 2 from both sides

-6=3x

divide by 3 on both sides

x=-2

y=-2-4=-6

y=4(-2)+2=-8+2=-6

8 0
2 years ago
A store pays $60 for shoes and sells them for $90. What is the percent mark up?
Anton [14]

Answer:

50%

Step-by-step explanation:

5 0
2 years ago
Please help me!
Sindrei [870]
Well, let's check if your inequality is true. We have to add the 3 scores up and divide them by 3 to know the average.

73 + 81 + 86 = 240
240 / 3 = 80

80%

That's true, now let's check 101.

73 + 81 + 101 = 255
255 / 3 = 85

85%

That's true.

Your inequality is correct.
5 0
3 years ago
(200 x 3) + (50 x 3)
m_a_m_a [10]

<em><u>200x3=600</u></em>

<em><u>50x3=150</u></em>

<em><u></u></em>

<em><u></u></em>

<em><u>600+150=750</u></em>

<em><u></u></em>

<em><u>750</u></em>

6 0
2 years ago
Read 2 more answers
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