cosA + cosB - cosC = -1 + 4cosA/2 cosB/2 sinC/2

Answer:

Step-by-step explanation:

(cos A+ cos B)-cos C

[tex]=2cos \frac{A+B}{2}cos \frac{A-B}{2}-cos C~~~...(1)\\A+B+C=180\\A+B=180-C\\\frac{A+B}{2}=90-\frac{C}{2}\\cos \frac{A+B}{2}=cos(90-\frac{C}{2})=sin \frac{C}{2}\\cos C=1-2sin^2\frac{C}{2}\\(1)=2 sin \frac{C}{2} cos \frac{A-B}{2}-1+2sin^2\frac{C}2}\\=2sin\frac{C}{2}[cos \frac{A-B}{2}+sin \frac{C}{2}]-1~~~...(2)\\\\now~again~A+B+C=180\\C=180-(A+B)\\sin\frac{C}{2}=sin(90-\frac{A+B}{2})=cos \frac{A+B}{2}\\(2)=2sin\frac {C}{2}[cos \frac{A-B}{2}+cos \frac{A+B}{2}]-1\\[/tex]

[tex]=-1+2sin\frac{C}{2}*2cos \frac{\frac{A-B}{2} +\frac{A+B}{2} }{2} cos \frac{\frac{A-B}{2} -\frac{A+B}{2} }{2} \\=-1+4sin\frac{C}{2} cos \frac{A}{2} cos\frac{-B}{2} \\=-1+4 cos \frac{A}{2} cos \frac{B}{2} sin \frac{C}{2}\\(cos(-B)=cos B)[/tex]

a radio station sells buttons and bumpers stickers at a local fair the buttons each cost $2.95 and the bumpers cost $3.50.the radio station sells at most $162.00 worth of buttons and bumpers.If x represents the number of buttons and y represent the number of bumper stickers,which inequality represents the scenario?

​59% of U.S. adults have very little confidence in newspapers. You randomly select 10 U.S. adults. Find the probability that the number of U.S. adults who have very little confidence in newspapers is ​ (a) exactly​ five, (b) at least​ six, and​ (c) less than four.

2. You are in a car traveling an average speed of 60 km/hr. The
total trip is 240 km. How long does the trip take?

The measures of two angles are represented by the expressions (5x + 24)° and (9x − 17)°. If the two angles are equal, what is the value of x?

PLEASE PLEASE HELP ME I WILL GIVE BRAINLIEST



For this expression, A= ____, B= ____, and C= ______

Which point is exactly 5 units from (-10, 4)?

1. When solving the equation: 8n -2 = 1 +n + 5 + 6, Response area could NOT be the first step that would yield a solution

3 divided by (?)= 36

What word phrase can you used to represent 5X +2

____ is one way to develop active immunity to a disease.
a.
Chemotherapy
c.
A vaccine
b.
Taking vitamins
d.
All of the above


Please select the best answer from the choices provided

A
B
C
D

A recording studio is forming a jazz quartet. How many different jazz quartets consisting of a saxophone player, an electric keyboard player, a bass player, and a drummer could it form

- 2x + 5 > -3
A.
X ²4
B. x > 4
C. X<-1
D. X > -1
A
Help!! I have to show my work too

Find the solution set of this inequality. Enter
your answer in interval notation using grouping
symbols.
|-8x + 4 = 12
Enten the correct answer.

Please help for brainliest and it’s is not 48

If y equals -5 when X equals 2, find Y when X equals 8?

The Lake Placid Town Council decided to build a new community center to be used for conventions, concerts, and other public events, but considerable controversy surrounds the appropriate size. To provide structure for the decision process, the council narrowed the building alternatives to three sizes: small, medium, and large. Everybody agreed that the critical factor in choosing the best size is the number of people who will want to use the new facility. The town council suggested using net cash flow over a 5-year planning horizon as the criterion for deciding on the best size. The following projections of net cash flow (in thousands of dollars) for a 5-year planning horizon have been developed.All costs, including the consultant's fee, have been included.
Demand Scenario
Center Size Worst Case Base Case Best Case
Small 400 500 660
Medium -250 650 800
Large -400 580 990
a) What decision should Lake Placid make using the expected value approach?
b) Construct risk profiles for the medium and large alternatives. Given the mayor's concern over the possibility of losing money and the result of part (a), which alternative would you recommend?
c) Compute the expected value of perfect information. Do you think it would be worth trying to obtain additional information concerning which scenario is likely to occur?

Please help will give brainliest

What is the factored form of x3 + 64?

(x2 + 8)(x + 8)

(x + 4)(x2 – 4x + 16)

(x – 4)(x2 + 4x + 16)

2/5 divided by 5/8 in SIMPLEST form

HELPPPPPPPPPPP PLEASEEEE.!!!!!!

Today, Jay ran 6 3/4 miles around the track and Nick ran 4 1/2 miles. How many times the length of Nick's was Jay's run?

56 In a video game, acquiring a flag is worth 2 points and
acquiring a golden saber is worth 5 points. In a single
game, Jill acquires 5 flags and 7 golden sabers, while
Amy acquires 2 flags and 13 golden sabers. Which of the
following matrix products represents the number of points
earned by Jill and Amy?

A teacher asked her pupils what their favorite school subject was 3 pupils said PE was their favorite subject How many said that maths was their favorite subject
HELP PLZZZZZZZZ
SOMEONE

Find the product. (0.7)(-5.8)

50 POINTS WILL GIVE BRAINLIEST Use the drawing tools to form the correct answer on the grid. Caroline is planting flowers in her garden. She plants her first 7 flowers in 4 minutes. After 12 minutes, she has planted 21 different flowers. Plot four data points and the line of best fit to model how long it takes Caroline to plant flowers.​​

Which rules define the function graphed below?

Which system of inequalities is shown?

Explain why the formulas for sample variance and population variance are different.
A. Variance is defined as the mean deviation, and, for a population, is computed as the sum of deviations divided by N. The sample variance will be biased and will consistently underestimate the corresponding population value.
B. Variance is defined as the mean squared deviation, and, for a population, is computed as the sum of squared deviations divided by N. The sample variance will be biased and will consistently underestimate the corresponding population value.
C. Variance is defined as the mean squared deviation, and, for a population, is computed as the sum of deviations divided by N. The sample variance will be biased and will consistently underestimate the corresponding population value.

A small pumpkin weighs 5 1 5pounds. What does 3 5of it weigh?

Solve proportion, if necessary round to nearest hundredth.