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3 years ago

Prove that :

Mathematics

2 answers:

anyanavicka [17]3 years ago

7 0

Answer:

$Question 3sinθ/ (1 - cotθ) + cosθ / (1 - tanθ) =sinθ / (1 - cosθ/sinθ) + cosθ / (1 - sinθ/cosθ) =sinθ/ [(sinθ - cosθ) / sinθ] + cosθ / [(cosθ - sinθ)/cosθ] =sin²θ/ (sinθ - cosθ) + cos²θ/(cosθ - sinθ) =sin²θ/ (sinθ - cosθ) - cos²θ/(sinθ - cosθ) =(sin²θ - cos²θ) / (sinθ - cosθ) =(sinθ + cosθ)(sinθ - cosθ) / (sinθ - cosθ) =sinθ + cosθ :D$

Step-by-step explanation:

Dimas [21]3 years ago

6 0

Answer:

<h3>Question 1</h3>

sec²θ + cosec²θ =
1/cos²θ + 1/sin²θ =
(sin²θ + cos²θ)/(sin²θcos²θ) =
1 / (sin²θcos²θ) =
[(sin²θ + cos²θ)/sinθcosθ]² =
(sinθ/cosθ + cosθ/sinθ)² =
(tanθ + cotθ)²

<h3>Question 2</h3>

(1 - tan²θ) / (1 + tan²θ) =
(1 - sin²θ/cos²θ) / (1 + sin²θ/cos²θ) =
(cos²θ - sin²θ) / (cos²θ + sin²θ) =
(cosθ + sinθ)(cosθ - sinθ) / 1 =
(cosθ + sinθ)(cosθ - sinθ)

<h3>Question 3</h3>

sinθ/ (1 - cotθ) + cosθ / (1 - tanθ) =
sinθ / (1 - cosθ/sinθ) + cosθ / (1 - sinθ/cosθ) =
sinθ/ [(sinθ - cosθ) / sinθ] + cosθ / [(cosθ - sinθ)/cosθ] =
sin²θ/ (sinθ - cosθ) + cos²θ/(cosθ - sinθ) =
sin²θ/ (sinθ - cosθ) - cos²θ/(sinθ - cosθ) =
(sin²θ - cos²θ) / (sinθ - cosθ) =
(sinθ + cosθ)(sinθ - cosθ) / (sinθ - cosθ) =
sinθ + cosθ

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A gardener already has four and one over 2 ft of fencing in his garage. He wants to fence in a square garden for his flowers. Th

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<h2>Answer:</h2>

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<h2>Step-by-step explanation:</h2>

Let's considerate the fact that the garden has a <u>square shape</u>.

<h3>1. Finding values of interest.</h3>

Amount of fence that the gardener already has: $4\frac{1}{2}$ ft.

Length of one side: $2\frac{3}{4}$ ft.

If one side measures $2\frac{3}{4}$ ft, and the square garden has 4 sides of equal length, because it's a square, then we must multiply the measure of one side by 4 to find the total length of fence needed:

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The gardener already has $4\frac{1}{2}$ , which equals $4 + \frac{1}{2}$ . Hence, the difference between the amount needed and the amount that the gardeneralready has will give us the remaining amount required. Let's do that:

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Source:
http://www.1728.org/combinat.htm

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