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Nastasia [14]
3 years ago
10

Prove that 1+cosθ+sinθ/1+cosθ-sinθ = 1+sinθ/cosθ

Mathematics
1 answer:
marusya05 [52]3 years ago
3 0

Step-by-step explanation:

(1 + cos θ + sin θ) / (1 + cos θ − sin θ)

Multiply by the reciprocal:

(1 + cos θ + sin θ) / (1 + cos θ − sin θ) × (1 + cos θ + sin θ) / (1 + cos θ + sin θ)

(1 + cos θ + sin θ)² / [ (1 + cos θ − sin θ) (1 + cos θ + sin θ) ]

(1 + cos θ + sin θ)² / [ (1 + cos θ)² − sin² θ) ]

Distribute and simplify:

(1 + cos θ + sin θ)² / (1 + 2 cos θ + cos² θ − sin² θ)

[ 1 + 2 (cos θ + sin θ) + (cos θ + sin θ)² ] / (1 + 2 cos θ + cos² θ − sin² θ)

(1 + 2 cos θ + 2 sin θ + cos² θ + 2 sin θ cos θ + sin² θ) / (1 + 2 cos θ + cos² θ − sin² θ)

Use Pythagorean identity:

(2 + 2 cos θ + 2 sin θ + 2 sin θ cos θ) / (sin² θ + cos² θ + 2 cos θ + cos² θ − sin² θ)

(2 + 2 cos θ + 2 sin θ + 2 sin θ cos θ) / (2 cos² θ + 2 cos θ)

(1 + cos θ + sin θ + sin θ cos θ) / (cos² θ + cos θ)

Factor:

(1 + cos θ + sin θ (1 + cos θ)) / (cos θ (1 + cos θ))

(1 + cos θ)(1 + sin θ) / (cos θ (1 + cos θ))

(1 + sin θ) / cos θ

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xeze [42]

<em>Hexagonal</em> implies that the <em>traffic sign</em> has six straight sides. But <u>dilating</u> it changes its <em>length</em> of sides, but not its angles. So that the <em>statement</em> that is <u>true</u> is option B.

i.e B. The <u>dilated</u> sign will have corresponding line segments that are <em>proportional</em> to those of the pre-image and <u>corresponding</u> angles that are congruent to that of the pre-image.

Dilation involves <u>increasing</u> or <u>decreasing</u> the line segments of a given shape by a <em>scale factor</em>. This process do not affect the measure of the internal <u>angles</u> of the shape.

Given a <u>hexagonal</u> traffic sign in the question, this implies that the traffic sign has six sides. <u>Dilating</u> it by a scale factor of 2.5 about its center would affect its <em>length</em> of sides. So that the <em>statement</em> that is <u>true</u> is option B.

i.e B. The dilated sign will have <u>corresponding</u> line segments that are proportional to those of the pre-image and <em>corresponding</em> angles that are congruent to that of the pre-image.

Visit: brainly.com/question/8285347

4 0
2 years ago
How do I solve this and please thoroughly explain the steps, please?
Zolol [24]

Answer:

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7 0
2 years ago
Please help me no one would help me i really need help due tomorrow.
irina [24]

Option B is correct.

Step-by-step explanation:

A triangle has vertices A(-3,-1), B(-6,-5), C(-1,-4). We need to find the transformation that will produce the triangle with vertices: A(3,-1), B(6,-5), C(1,-4)

Seeing the vertices of transformed triangle, we observe that the x-coordinate of vertices has been opposite of that in the original vertices, while y-coordinate remains same.

This shows it is reflection over y-axis. In which x-coordinate becomes the negative (opposite) of original coordinate while y-coordinate remains the same.

So, Option B is correct.

Keywords: Transformation of Triangles

Learn more about Transformation of Triangles at:

  • brainly.com/question/9381523
  • brainly.com/question/2415963
  • brainly.com/question/3779181

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7 0
2 years ago
How many sides does a heptagon have
BARSIC [14]

A heptagon is a polygon.

It has 7 sides

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3 0
3 years ago
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C. 16

To find the mode, you find the highest number in the data set, then you subtract the highest number (21) from the lowest number in the data set (4). So the mode would be 16.
5 0
3 years ago
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