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deff fn [24]
3 years ago
14

IF A+B+C=Π prove that sin(3A)+sin(3B)+sin(3C)=-4cos(3A÷2)cos(3B÷2)cos(3C÷2)​

Mathematics
1 answer:
Hunter-Best [27]3 years ago
4 0

Answer:

LHS of the given equation is:

sinθ+sin3θ+sin5θ+sin7θ=(sinθ+sin7θ)+(sin3θ+sin5θ)=2sin8θ2.cos6θ2+2sin8θ2.cos2θ2   [since sinC+sinD=2sinC+D2.cosC−D2=2sin4θ.cos3θ+2sin4θ.cosθ=2sin4θ.[cos3θ+cosθ]       [since cosC+cosD=2cosC+D2.cosC−D2=2sin4θ.[2cos2θ.cosθ]=4cosθ.cos2θ.sin4θsinθ+sin3θ+sin5θ+sin7θ=(sinθ+sin7θ)+(sin3θ+sin5θ)=2sin8θ2.cos6θ2+2sin8θ2.cos2θ2   [since sinC+sinD=2sinC+D2.cosC-D2=2sin4θ.cos3θ+2sin4θ.cosθ=2sin4θ.[cos3θ+cosθ]       [since cosC+cosD=2cosC+D2.cosC-D2=2sin4θ.[2cos2θ.cosθ]=4cosθ.cos2θ.sin4θ

any more help just ask :)

Step-by-step explanation:

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484,343 rounded to the nearest thousand
Semmy [17]

Answer:

484,000

Step-by-step explanation:

The hundreds place is less than 5 so you round down.

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3 years ago
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Mumz [18]

Step-by-step explanation:

18h=252

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5 0
3 years ago
I NEED HELP PLEASE !
MrRa [10]

Answer:

x = 4, -2 1/2

Step-by-step explanation:

factors:

(2x + 5) (x - 4)

set each factor equal to zero:

2x + 5 = 0

2x = -5

x = -5/2

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6 0
3 years ago
If arc EF = 151°, find mEDF.
user100 [1]
There is a theorem that says that this angle (formed by thre points on the circumference) is half such arc called EF.

We can deduct it as well.

1) Call O the center of the circle. The central angle (EOF) = arc EF = 151°

2) Draw a chord from F to D and other chord from D to E.

You have constructed two triangles, FOD and DOE.

3) Triangle FOD has two sides equals (because both are the radius of the circcle). Then, this is an isosceles triangle and it has two angles of the same measure. Call this measure a.

4) Triangle DOE is also isosceles, for the same reason explained in the poiint 3. Call the measure of its equal angles b.

5) The sum of the angles of the two triangles is 180° + 180 ° = 360°.

This is a + a + b + b + (360 - central angle) = 360°

=> 2a + 2b = central angle
=> 2(a+b) = cantral angle
=> (a+b) = central angle / 2 = 151° / 2 =71.5°

(a+b) is the angle that you are looking for.

Then the answer is 71.5°

 
4 0
3 years ago
What visualization should be used to show how many observations of a certain value have been made?
Levart [38]
<span>A bar graph or pie chart would be good visualization method to demonstrate how many observations of a certain value have been made. The bar graph and pie chart would also provide slightly different perspectives on the proportion of observed values recorded.</span>
6 0
3 years ago
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