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vladimir2022 [97]
3 years ago
11

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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<h3>How to solve the equation</h3>

A real-life word problem that corresponds to the equation x² = 144 will be that the area of a farmer's square garden is 144 square feet. What is the length of the garden?

In this case, the length of the garden will be the square root of 144. This will be calculated thus:

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