(cosA+cosB)²+(sinA+sinB)²=4cos²(A-B/2)​

Answers

Answer 1
Solution:
LHS = (cosA+cosB)²+(sinA+sinB)²
= (cos²A+2cosAcosB+cos²B)+
(sin²A+2sinAsinB+sin²B)
/* By algebraic identity:
(x+y)² = x²+2xy+y² */
Rearranging the terms, we get
= (cos²A+sin²A)+(cos²B+sin²B)+2(cosAcosB+sinAsinB)
= 1+1+2cos(A-B)
________________________
we know that,
i) cos²x + sin²x = 1
ii) cosxcosy+sinxsiny = sin(x-y)
________________________
= 2+2cos(A-B)
= 2[1+cos(A-B)]

=
=
=$RHS$
Therefore,
(cosA+cosB)²+(sinA+sinB)²
=
••••



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Related Questions

please help me oout with this one and dont just put a random answer so u can get points its not like u can buy a CAR with it lol

Answers

Answer:

V - 1099.55742876

SA - 769.690200129

Step-by-step explanation:

The volume of a cone is denoted by the formula:

V = 1/3 * h * pi * r^2

We can substitute in the values we are given:

V = 1/3 * 10.5 * pi * 10^2

V = 3.5 * 100 * pi

V = 350pi

This is about: 1099.55742876

The formula for the surface area of a cone is:

SA = pi * r^2 + pi * r * s

We can substitute what we have:

SA = pi * 10^2 + pi * 10 * 14.5

SA = 100 pi + 145 pi

SA = 245 pi

This is about: 769.690200129

What value of x makes the equation x+ 38 = 72 true?​

Answers

Answer:

x = 34

Step-by-step explanation:

Given

x + 38 = 72 ( subtract 38 from both sides )

x = 34

Answer:

X=34

Step-by-step explanation:

Well, what you can do is bring the 38 to the other side and make it negative so you can subtract 38 with the 72. The 72-38 is= 34 and so x= 34

x+38=72

x=72-38

x=34

Hope this helps! ^^

There are 3000 student in the school 30% of the student are girls find
A) The total number of girl
B) The total number of student ​

Answers

Step-by-step explanation:

3000 [tex] 3000 \div 30 = 1000[/tex][tex]3000 \times 30 = 90000[/tex]
A) 3000 * 30% = 3000 * 0.3 =900

What is the sequence of transformations?
9 Pts
A

Answers

Answer:

Its a

Step-by-step explanation:

It takes Chris 30 minutes to walk to work. If he drives, it takes him 1/3 of that time.

What is the latest time that Chris can leave to drive to work and arrive by 8:00?

Answers

Answer:

7:50

Step-by-step explanation:

cause.....

30/3=10

8:00- 10 min = 7:50

Josh has drawn a map of three destinations he wants to visit. What is the distance between destinations A and B

Answers

Answer:

73.5

Step-by-step explanation:

Please find the complete question in the attached image

Remember the notation SOHCAHTOA

We would be using cos because we have been given the hypotenuse and we are to determine the adjacent value

cos 37 = adjacent / hypotenuse

cos 37 = adjacent / 92

0.7986 = adjacent / 92

adjacent = 0.7986 x 92 = 73.5

A chemist has a solution that has 0.55 grams of alcohol per 1 mL of solution. If she needs 975 mg of
alcohol, how much solution does she need? Round your answer to the nearest hundredth. (1 gram = 1,000
milligrams)

Answers

Answer: 5000000

Step-by-step explanation:

0.55 x 1

975 = 5000000

If f(x)= x/1+x, what is the value of f(x+h)

Answers

Answer:

f(x+h)=

Step-by-step explanation:

f(x+h)=x+h+x+h

2h+2x2(h+x)

stay safe healthy and happy.

Graph the line given by the equation: 2x+4y=-3

Answers

2x+4y=-3 (put 2x on other side)
4y=-3-2x (/ all sides by 4)
y= -3/4 -2/4x (and simplify)
y= -1/2x -3/4

I hope this helped!

Let alpha and beta be the radiant measures of two angles. Then sin left parenthesis 2 alpha plus 2 beta right parenthesis is equal to

Answers

Answer:

sin2αcos2β + cos2αsin2β

Step-by-step explanation:

Given that

sin(A+B) = sinA cos B + cos A sinB

According to the question;

sin(2α+2β) = sin2αcos2β + cos2αsin2β

where A =  2α and B = 2β

Attendance at state park throughout the year is found to be periodic and can be modeled by a sine function. The attendance ranges from a low approximately 1,00,000 visitors in september to a high of approximately 2,00,000 visitors in march. If t is the month number, where t=1 is january, and N(t)is the attendance, in millions, of visitors, which of the functions can be used to model this behavior A: N(t)=0.5sin(π/6 t)+1.5 B: N(t)=1sin(π/6 t)-1 C: N(t)=0.5sin(2πt)+1.5 D: N(t)=1.5sin(π/6 t)+0.5

Answers

Answer:

A. N(t) = 0.5·sin((π/6)·t) + 1.5

Step-by-step explanation:

The given parameters are;

The model of the periodic function = Sine function

The low of the attendance = 1,000,000

The month of the low in attendance = September

The high in attendance = 2,000,000

The month number = t,

The month of January is represented by, t = 1

N(t) = The attendance in millions of visitors

The generic sine function which is given as y = a·sin(b·x + c) + d, ranges from -1 to 1

Period = 12 = 2·π/b

∴ b = 2·π/12 = π/6

c = 0

a = The amplitude = (The maximum - The minimum)/2 = (2,000,000 - 1,000,000)/2 = 500,000

Therefore, a = 0.5×1,000,000 = 0.5·N(t)

Therefore, given that the minimum, [tex]N(t)_{min}[/tex] = 1, we have;

For sin(b·x + c) = -1, a·sin(b·x + c) = -0.5, for the minimum of 1,000,000 = 1 × 1,000,000, we have;

a·sin(b·x + c) + d = 1

∴ -0.5 + d = 1

d = 1.5

Therefore, we have;

N(t) = 0.5·sin((π/6)·t) + 1.5

Answer:

N(t) = 0.5sin((π/6)t) + 1.5

Step-by-step explanation:

Two phone companies one is 11/+.16/ min And another is 20+.11/min How many minutes will make both equal amounts

Answers

Answer:

Company one charges $11 + $0.16 per min.

Then if you talk for x minutes, the cost will be:

C₁(x) = $11 + ($0.16 per min)*x

For company two, the prize is $20 + $0.11 per min, and if yo talk for x minutes, the cost will be:

C₂(x) = $20 + ($0.11 per min)*x

Now we want to find the value of x, the number of minutes, such that the cost is the same with both companies.

C₁(x) = C₂(x)

$11 + ($0.16 per min)*x = $20 + ($0.11 per min)*x

($0.16 per min)*x - ($0.11 per min)*x = $20 - $11

($0.05 per min)*x = $9

x = $9/($0.05 per min) = 180 mins

If you speak for 180 minutes, the cost is the same in both companies.

I need help with this!

Answers

Answer:

4.25

Step-by-step explanation:

Since this is a parallelogram, the parallel sides have the same value.

And since the perimeter of a parallelogram is all of the sides combined, this means

WR + RJ + JS + WS, or

5x + 5x + 3x + 2 + 3x +2 = 16x + 4

The perimeter is 16, so

16x + 4 = 16

16x = 12

x = 0.75

Substitute into 3x + 2, or WS.

2.25 + 2 = WS

WS = 4.25

Step-by-step explanation:

perimeter of parallelogram =16

2(WR+RJ)=162(5x+3x+2)=1610x+6x+4=1616x=16-4x=12/16x=3/4

so value of WS=3x+2

3×3/4+24.25cm

hope it helps

stay safe healthy and happy.

The area of a circle is 28.74cm2.
Find the length of the radius rounded to 2 DP.

Answers

Answer:

3.025 = 3.03

Step-by-step explanation:

A = (3.14)(r)(r)

28.74/3.14 = 9.152866

3.025 = r

For what values of x and y are the triangles congruent​

Answers

Answer: b maybe

Step-by-step explanation:

Answer:

D.) x=5, y=2

Step-by-step explanation:

Triangle ABC

Hypotenuse, 2(5) + 3 = 13

Base,4(2)+2= 10

Triangle DEF

Hypotenuse, 3(5) - 2 = 13

Base, 9(2) - 8 = 10

A population of 12,000 fish has a growth rate of 4% each year. Write a model for the situation. How many years will it take of the population to reach 20,000

Answers

Answer:

13years

Step-by-step explanation:

Using the formula for calculating the compound interest expressed as;

A =P(1+r)^n

P = 12000

rate r  = 4% = 0.04

Amount after 4 years A = 20,000

Substitute into the formula and solve for p

20,000 = 12,000(1+0.04)^t

20,000/12000 = (1.04)^t

1.67 = (1.04)^t

Take the ln of both side

ln1.67 = ln(1.04)^t

ln1.67 = t ln 1.04

t = ln1.67/ln1.04

t = 0.5108/0.0392

t = 13.03

hence it will take approximately 13years to reach 20,000

Solve for x. Round your answer to the nearest tenth.

Answers

Answer:

x = 11.1

Step-by-step explanation:

Cosine theta = adjacent/hypotenuse

cos 42 = x/15

x = 15 cos 42

x = 11.1

Answer is 11.1 I hope it helps

PLEASE ASAP ILL GIVE BRAINLIEST.

Answers

Answer:

A basket ball being held

Step-by-step explanation:

Hope this helps you out

in 2decimal places 39.98015​

Answers

Answer:

39.98

Explanation:

39.98015​

0 < 5, so 2nd decimal stays at 8

Answer:39.98

Step-by-step explanation:

Hey! I’m not exactly sure what you’re asking, but if the question is how to write that number in only two decimal places, it would be 39.98. We would round it up or down in the hundredths place because that is the second decimal place. Since the number behind the 8 is 0, we can’t round up or down so we would just leave it how it is and cut off the rest.

Hope this helped! :D

Sorry it I didn’t answer what you were asking! You can comment and I will answer any further questions!

ncmmkksms ndsjms sks dnc dd jdjsks sbds

Answers

jdsfjsfjsdj jsdf jsgd jj ej jjs sejr

what term is used to best describe the spread of the data set?
A. Median
B. Mode
C. Mean
D. Range

Answers

I'm not that sure but I think the answer is Median (A)

What is the value of the expression 2 x 33 + 17 + 5 x 8

Answers

Answer:

Correct answer of this question is 123

Answer:

123

Step-by-step explanation:

sounds funny but its true

(2x33)+17+(5x8)

do parenthensies first

2x33=66

5x8=40

40+66=106=17=123

Nate has 1.44 pounds of meat. He uses 0.24 pound of meat to make one hamburger. How many hamburgers can Nate make with the meat he has?

Answers

Answer: 6

Step-by-step explanation: 1.44 divided by 0.24 equals 6

An explanation is required or else not brainliest.

Answers

Answer:

16 meters

Step-by-step explanation:

[tex] In\: \odot F, \: \overline {RS} [/tex] is tangent to the circle at point R and FR is radius.

[tex] \therefore RF\perp RS[/tex] (Tangent radius theorem)

[tex] \therefore m\angle FRS = 90\degree [/tex]

So, [tex] \triangle FRS[/tex] is right angled triangle and FS is its hypotenuse.

Let FR = FT = r

FS = FT + ST = r + 9

Now, by Pythagoras theorem:

[tex]FR^2 + RS^2 = FS^2 \\ \therefore r^2 + (15)^2 = (r + 9)^2 \\ \therefore \cancel{ r^2} +225 = \cancel{ r^2} + 18r + 81\\ \therefore \: 225 = 18r + 81 \\ \therefore \: 225 - 81= 18r \\ \therefore \: 144= 18r \\ \therefore \: r = \frac{144}{18} \\ \therefore \: r =8 \: m\\ \implies \: d = 2r = 2(8) = 16 \: m[/tex]

Thus, the diameter of the fountain is 16 meters.

Which equation represents the line that is perpendicular to y = 5x + 4 and passes through the point (-5, 2)?

Answers

Answer:

y = (-1/5)x + 1

Step-by-step explanation:

The slope of this perpendicular line is the negative reciprocal of the slope of the given line y = 5x + 4:  -1/5.

Applying the slope-intercept form of the equation of a line, we get:

2 = (-1/5)(-5) + b, or:

2 = 1 + b

Therefore, b = 1 and the desired equation is:

y = (-1/5)x + 1

Please, if you are given answer choices, share them.

Use the distributive property to remove the parentheses. 5(v+6)

Answers

Answer:

5 x 6v

Step-by-step explanation:

PLLLLLLLS HELP WILL GIVE BRAILEST 20 POINTS
colby is standing next to a water tower, he is 6ft tall and casts a 3 foot shadow.

if the water tow cast a 60 foot tall shadow, how tall is the tower?

30
120
180
240

Answers

Answer:

the water tower casts 60 ft shadow its 120 ft tall

Step-by-step explanation:

Answer:

180 I hope this is the correct answer

Help please. It’s due tomorrow and I have in person class and I actually don’t understand. (It’s ok if not)

Answers

Answer:

I would’ve worked it out but it’s been years

Step-by-step explanation:

use the inverse operation to solve the following equation w + 125.2 = 255​

Answers

Answer:

w=129.8

Step-by-step explanation:

w + 125.2 = 255​

                  -125.2

w=225-125.2

w=129.8

Answer:

Hope this helps please mark me as branlist.

Step-by-step explanation:

Subtract 125.2 from both sides:

w=125.2=255

w=125.2-125.2=255-125.2

w=255-125.2

w=129.8

what's the value of "x"? Show all your work. ​

Answers

Answer:

x=9

Step-by-step explanation:

a²+b²=c²

x²+6²=(√117)²

x²+36=117

x²=81

x=9

Answer:

3[tex]\sqrt{17}[/tex] or 12.37 cm

Step-by-step explanation:

use the Pythagorean Theorem:

6² + [tex]\sqrt{117}[/tex]² = x²

36 + 117 = x²

x² = 153

x = [tex]\sqrt{153}[/tex] which is [tex]\sqrt{9}[/tex][tex]\sqrt{17}[/tex] or 3[tex]\sqrt{17}[/tex]

in decimal form, 'x' is approx 12.37

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