1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
aleksley [76]
3 years ago
14

Please help me!!!!!​

Mathematics
1 answer:
denpristay [2]3 years ago
6 0

Answer:  see proof below

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

Given: A + B + C = π               → A = π - (B + C)

                                               → B = π - (A + C)

                                               → C = π - (A + B)

Use Sum to Product Identity: sin A - sin B = 2 cos [(A + B)/2] · sin [(A - B)/2]

Use the following Cofunction Identity: cos (π/2 - A) = sin A

<u>Proof LHS → RHS:</u>

LHS:                        sin A - sin B + sin C

                             = (sin A - sin B) + sin C

\text{Sum to Product:}\quad 2\cos \bigg(\dfrac{A+B}{2}\bigg)\cdot \sin \bigg(\dfrac{A-B}{2}\bigg)+2\cos \bigg(\dfrac{C}2{}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)

\text{Given:}\qquad 2\cos \bigg(\dfrac{\pi -(B+C)}{2}+\dfrac{B}{2}}\bigg)\cdot \sin \bigg(\dfrac{A-B}{2}\bigg)+2\cos \bigg(\dfrac{C}2{}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)\\\\\\.\qquad \qquad =2\cos \bigg(\dfrac{\pi -C}{2}\bigg)\cdot \sin \bigg(\dfrac{A-B}{2}\bigg)+2\cos \bigg(\dfrac{C}2{}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)

.\qquad \qquad =2\cos \bigg(\dfrac{\pi}{2} -\dfrac{C}{2}\bigg)\cdot \sin \bigg(\dfrac{A-B}{2}\bigg)+2\cos \bigg(\dfrac{C}2{}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)

\text{Cofunction:} \qquad 2\sin \bigg(\dfrac{C}{2}\bigg)\cdot \sin \bigg(\dfrac{A-B}{2}\bigg)+2\cos \bigg(\dfrac{C}2{}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)

\text{Factor:}\qquad 2\sin \bigg(\dfrac{C}{2}\bigg)\bigg[ \sin \bigg(\dfrac{A-B}{2}\bigg)+\cos \bigg(\dfrac{C}{2}\bigg)\bigg]

\text{Given:}\qquad 2\sin \bigg(\dfrac{C}{2}\bigg)\bigg[ \sin \bigg(\dfrac{A-B}{2}\bigg)+\cos \bigg(\dfrac{\pi -(A+B)}{2}\bigg)\bigg]\\\\\\.\qquad \qquad =2\sin \bigg(\dfrac{C}{2}\bigg)\bigg[ \sin \bigg(\dfrac{A-B}{2}\bigg)+\cos \bigg(\dfrac{\pi}{2} -\dfrac{(A+B)}{2}\bigg)\bigg]

\text{Cofunction:}\qquad 2\sin \bigg(\dfrac{C}{2}\bigg)\bigg[ \sin \bigg(\dfrac{A-B}{2}\bigg)+\sin \bigg(\dfrac{A+B}{2}\bigg)\bigg]

\text{Sum to Product:}\qquad 2\sin \bigg(\dfrac{C}{2}\bigg)\bigg[ 2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad \qquad =4\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)

\text{LHS = RHS:}\quad 4\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)=4\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)\quad \checkmark

You might be interested in
When looking at the median of a data set, what information do you get when looking at the median?
cestrela7 [59]
You get the middle of all the data while looking at the median of a data set!

I hope this helped! Mark me Brainliest! :) -Raven❤️
7 0
3 years ago
Kenji had 1/4 of a pizza left over. He ate 1/2 of the leftovers. How much of a pizza did he eat?
german

Answer:

1/8

Step-by-step explanation: 2/8=1/4

3 0
2 years ago
Read 2 more answers
Meh needs some help once again
Ymorist [56]
1:1 because you simplify
7 0
2 years ago
Explain an example of how taking an amount (for example, $20), decreasing it by 40% and then increasing that amount by 40% does
Likurg_2 [28]

Answer:

See below

Step-by-step explanation:

What we can do is try it out.

20*0.6=12

since 0.6 is left

now we increase 12 by 40, or multiply it by 1.4

12*1.4= 16.8

See what is happening here is that at first when we are decreasing it by 40 percent, we are taking 40 percent of 20. However, when we increase that amount by 40 percent, we are now increasing 40 percent of 20 by 40 percent, or increasing 16 by 40 percent. Therefore, we will not get the original amount.

4 0
3 years ago
Simon drove through some roadworks where the speed limit was 50 mph. Two cameras recorded the time taken to travel 1200 m throug
Tom [10]

Answer:

Speed = 21.43m/s

Step-by-step explanation:

Given

Distance = 1200m -- of the roadworks

Time\ Recorded = 56s

Required

Determine the speed

In this case:

Speed = \frac{Distance\ of\ Roadword}{Time\ Captured}

Speed = \frac{1200m}{56s}

<em></em>Speed = 21.43m/s<em> --- approximated</em>

3 0
3 years ago
Other questions:
  • Round 964323 to the nearest thousand
    7·2 answers
  • If f(x) = x2 + 1 and g(x) = x -4, which value is equivalent to (f•g)(10)?
    11·1 answer
  • Helppp
    15·1 answer
  • How do I simplify (y^3)^3 without parentheses?
    14·2 answers
  • Mable’s cookie recipe calls for 3/4 of a cup of flour. Her mother’s recipe calls for 2/3 as much as Mable’s. How many cups of fl
    10·1 answer
  • . In the commercial production of sugar (sucrose), the product crystals are washed and centrifuged to partial dryness. The cryst
    7·1 answer
  • I will give brainliest to whoever answers this correctly
    7·2 answers
  • A figure is dilated by a scale factor of 6. Which ​ of the following is true about the figure and its dilation? there is no phot
    10·1 answer
  • A number b is at least - 3.
    5·2 answers
  • Help someone please
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!