Mathematics College

if a + b equal to pi by 4 then prove that 1 + cot a into 1 + cot B equal to 2 into cot a into cot b​

If A + B Equal To Pi By 4 Then Prove That 1 + Cot A Into 1 + Cot B Equal To 2 Into Cot A Into Cot B

Answers

Answer 1

Answer:

(cotA − 1) (cotB − 1) = 2

Step-by-step explanation:

A+B= π/4 = 180°/4 = 45°

A+B=45°

∴ cot(A+B)=cot45°

∴ cotBcotA−1 / (cotB+cotA) = 1

⇒cotB + cotA = cotBcotA = 1

⇒cotB + cotA − cotBcotA + 1 = 0

⇒cotBcotA − cotB − cotA − 1 = 0

⇒cotBcotA − cotB − cotA − 1 + 2 = 0+2

⇒cotBcotA − cotB − cotA + 1 = 2

⇒cotB(cotA − 1) (cotA − 1) = 2

⇒(cotA − 1) (cotB − 1) = 2

Proved

Related Questions

Given the set of numbers, 2, 3, 4, 8, 10 with mean = 6 The Second moment about the mean for this set is?​

Answers

Answer:

Given,

2,3,4,8,10

ex=2+3+4+8+10+x

=27+x

mean=6

no of data=5

now,

mean = ex/n

or,6=27+x/5

or,5×6=27+x

or,30=27+x

or,30-27=x

3=x

simplify [tex]y^{-3}[/tex]y^-3

Answers

Answer:

[tex]\frac{1}{y^{3} }[/tex]

Step-by-step explanation:

1/y3 is your answer

Use the formula to evaluate the infinite series. Round to the nearest hundredth if necessary.

Formula for a converging infinite series. a1 is the first term and r is the common ratio.

A. 4
B. 1.33
C. 5.33

Answers

Answer:

4

Step-by-step explanation:

This is an infinite geometric series. This has a sum of  

Where

a is the first term, and

r is the common ratio (one term divided by the previous term)

Let's figure out the first 2 terms by plugging in n = 1 first and then n = 2 for the series.

Help help math math math

Answers

Answer:

[tex]slope = \frac{20 - 16}{5 - 3} [/tex]

[tex] = \frac{4}{2} [/tex]

[tex] = 2 \: is \: the \: answer[/tex]

The slope of the equation is 2.

What is the slope of an equation?

The slope of an equation shows a gradient line that measures the steepness of the line.

It can be expressed by using the formula:

[tex]\mathbf{slope = \dfrac{\Delta y}{\Delta x}}[/tex]

[tex]\mathbf{slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]

From the parameters given;

The change in y distance from y2 to y1 The change in x distance from x2 to x1

[tex]\mathbf{slope = \dfrac{20-16}{5-3}}[/tex]

[tex]\mathbf{slope = \dfrac{4}{2}}[/tex]

slope = 2

Learn more about the slope of the equation here:

https://brainly.com/question/3493733

The graph of the function f is shown below
Find f(0)
​

Answers

Answer:

2

Step-by-step explanation:

Write that down before Katie deletes it. There is no work to show, only read the graph.

Solve. 6 Everyone at a park was either hiking or riding a bike. There were 24 more hikers than bike riders. If there were a total of 100 people at the park, how many were hiking?​

Answers

b r = 178 + h;

b r + h = 676;

then, 178 + 2h = 676 => h = 498/2 = 249 => b r = 178 + 249 = 427

Answer:

676

Step-by-step explanation:

h=b+178=427

b=b=249

-------------

(b+178)+b=676

2b+178=676

2b=498

b=249

-------------

249+427=676

Kaneppeleqw and 2 more u

Identify the variation as direct, inverse, joint or combined.
V =nr2h
O direct
O inverse
O joint
combined

Answers

Answer:

Sorry po just seen your email and I

Answer:

Sorry po just seen your email and I

Simplify. −3(2.1x−6.72)+0.8 −5.5x+20.16 −6.3x−5.92 −5.5x−19.36 −6.3x+20.96

Answers

Answer: -29.9x+37.6

Step by step answer: Use PEMDAS rule

−3(2.1x−6.72)+0.8 −5.5x+20.16 −6.3x−5.92 −5.5x−19.36 −6.3x+20.96

Use the distrubitive property

-6.3x+20.16+0.8 −5.5x+20.16 −6.3x−5.92 −5.5x−19.36 −6.3x+20.96

-6.3x+20.96−5.5x+20.16 −6.3x−5.92 −5.5x−19.36 −6.3x+20.96

Reorder/group x's and whole numbers

-6.3x-5.5x-6.3x-5.5x-6.3x+20.96+20.16-5.92-19.36+20.96

-6.3x-5.5x-6.3x-5.5x-6.3x+41.12-5.92-19.36+20.96

-6.3x-5.5x-6.3x-5.5x-6.3x+41.12-5.92+1.6

-6.3x-5.5x-6.3x-5.5x-6.3x+41.12-3.52

-11.8x-6.3x-5.5x-6.3x+41.12-3.52

-18.1-5.5x-6.3x+41.12-3.52

-23.6x-6.3x+41.12-3.52

-29.9x+41.12-3.52

-29.9x+37.6

Order each set of rational numbers from least to greatest 2.1,-0.3,0.261,-2.5

Answers

Answer:

i think -2.5 -0.3 0.261 2.1

How do you find the Dilation of 1.5? Also how would you write the Algebraic representation? ​

Answers

Answer:

Multiply each coordinate point by 1.5, y=1.5x

Step-by-step explanation:

Find the values of the variables.
isosceles trapezoid
Side measures are: 4, 2x, 2x + 2 and 4x +3
X=

Answers

Answer:

x = 1

Step-by-step explanation:

Given isosceles trapezoid.

Its congruent sides are 4 and (2x + 2):

2x + 2 = 4

Solve for x:

2x = 2x = 1

What is one five eights plus one two eights?

Answers

Answer:

5/8

Step-by-step explanation:

Answer: I think it's 2 7/8 lemme know if i'm wrong

Step-by-step explanation:

What is the product of 3.45 x
(1.93 x 10^4)

Answers

Answer:

66,585

Step-by-step explanation:

First, solve 10^4, which is 10,000. Then, do 1.93x10,000 and get 19300. Finally, multiply 19300 by 3.45 to get 66,585.

Always use pemdas and hope this helped!

I need help on math please

Answers

Answer:

if i correct pls comment I think it is 33


Mariana's office recycled a total of 9 kilograms of paper over 3 weeks. After 4 weeks,
how many kilograms of paper will Mariana's office have recycled? Solve using unit rates.

Answers

Answer:

9 kg per 3 weeks = 3 kg per week

Therefore, after 4 weeks it is (4 * 3) kilograms or 12 kilograms

Step-by-step explanation:

The aquarium owns two research boats that will be docked next to the new building. The Delfino recently took 5 hours to cover 57.5 miles of shoreline. On its last research voyage, the Balina surveyed 54 miles in 4.5 hours. Which boat is faster?

The Delfino can travel at a rate of ______________ miles per hour (mph).

The Balina can travel at a rate of ______________ miles per hour (mph).

Answers

Answer:

The Balina is faster than the Delfino.

Step-by-step explanation:

Divide the amount of miles covered by the amount of hours it took for each one.

For the Delfino:

57.5 / 5 = 11.5

For the Balina:

54 / 4.5 = 12

You're welcome T^T

An element with mass 330 grams decays by 25.5% per minute. How much of the
element is remaining after 5 minutes, to the nearest 10th of a gram?

Answers

Answer:

After 5 minutes, it remains 75.73 grams of mass.

Step-by-step explanation:

Each minute, the mass is decreased by a 25.5%. So, we can find the mass after each minute period.

First minute.

330gr - 0.255 (330gr)= (330 - 84.15)gr = 245.85gr

Second minute.

245.85 - 0.255 (245.85) = 245.85 - 62.69 = 183.16gr

Third minute.

183.16 - 0.255 (183.16) = 183.16- 46.70= 136.45gr

Fourth minute.

136.45- 0.255 (183.16) - 136.45 - 34.80= 101.65gr

Fifth minute.

101.65 - 0.255 (101.65)= 101.65 - 25.92= 75.73gr

Therefore, after 5 minutes, it remains 75.73 grams of mass.

Whta is the geometric mean of 5 and 36

Answers

Step-by-step explanation: 2 × 18 = 36. Then (as there are two numbers) take the square root: √36 = 6. this is for 36

Answer: 13

Step-by-step explanation:√(5 × 36) = 13.416407865

Katerina is a real estate agent. Katerina works on a 4% commission. She earns a $4200
commission. What was the value of the house that she sold?

Answers

Answer:

105,000

Step-by-step explanation:

help me out with this question .?​

Answers

1

Step-by-step explanation:

true ya false you say me

A pattern rule is square, triangle, circle, oval. What is the 50th shape?

Answers

Patterns are used to represent sequence of numbers.

The shape at the 50th position is a triangle

The pattern rule is given as: square, triangle, circle, oval.

The number of shapes (n) is given as:

[tex]n =4[/tex]

So, the 50th shape is calculated using the following absolute operator

[tex]Shape = 50\%4[/tex]

i.e. divide 50 by 4, and take note of the remainder.

When 50 is divided by 4, the remainder is 2

So, we have:

[tex]Shape =2[/tex]

This means that, the shape at the 50th position is the same shape at the 2nd position.

Hence, the shape is triangle

Read more about pattern at:

https://brainly.com/question/24050043

Find all real values of $x$ such that $x^2-5x + 4=0$.

Answers

Answer:

x=4 && x=1

Step-by-step explanation:

x^2 - x - 4x + 4=0

x(x-1) - 4(x - 1)=0

(x-4)(x-1)=0

X=4 and x=1

All real values of $x$ such that $x²-5x + 4=0$ will be x=4 and x=1.

What is the equation?

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, the quadratic equation is, x²-5x+4=0

Any equation of form ax²+bx+c=0  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

We have to find the value of x as,

x²-5x + 4=0

x² - x - 4x + 4=0

x(x-1) - 4(x - 1)=0

(x-4)(x-1)=0

X=4 and x=1

Thus, all real values of $x$ such that $x²-5x + 4=0$ will be x=4 and x=1.

Learn more about the equation here,

https://brainly.com/question/10413253

#SPJ6

Mark which expressions represent the distance between 46 and-15

Answers

|-15-46|
...........

5-x=3
Work out the value of 3x2

Answers

Answer:

No

Step-by-step explanation:

5-X=3

X=5+3

X=8

5-8=3

Which expression shows how 8⋅54 can be rewritten using the distributive property?




4⋅50+4⋅4

50⋅8+50⋅4

8⋅50+8⋅4

8⋅50+8⋅54

Answers

Answer:

8 • 54=8 • 50 + 8 • 4

Option C is the right answer

Step-by-step explanation:

Answer:

C I think, sorry if I'm wrong

LAST ATTEMPT IM MARKING AS BRAINLIEST!! (Finding missing sides- similar triangles Algebraic practice )

Answers

143 / 6x+12 = 132 / 72
143 / 6x+12 = 11 / 6

crossmultiply:
66x + 132 = 858
66x = 726
x = 11

Answer:

[tex] \frac{vw}{gf} = \frac{uv}{hg} [/tex]

[tex] \frac{72}{132} = \frac{6x + 12}{143} [/tex]

[tex] \frac{6}{11} = \frac{6x + 12}{143} [/tex]

Now we cross multiply

6×143=11(6x+12)

858=66x+132

858-132=66x

726=66x

x=11

You have a balance of $4,500 on your credit card. The interest rate is 12% (1% per month). The late payment fee is $40. You miss a payment. What are your fees plus interest for the month?

Answers

Answer:

multiplying 4500 by .01. This gave me $45 as in interest. Then I added the payment fee, $40. 40+45 is 85,

Step-by-step explanation:

WILL GIVE BRAINLIEST

Answers

Answer:

it is d

Step-by-step explanation:

What is the answer ??

Answers

Answer:

first of all take LCM OF THE denominator and solve it as shown

Given a conditional statement p → q, find the inverse of its inverse, the inverse of its converse, and the inverse of its contrapositive.

Answers

The inverse of an implication p ⇒ q is ¬p ⇒ ¬q.

The converse of p ⇒ q is q ⇒ p.

The contrapositive of p ⇒ q is ¬q ⇒ ¬p.

Then

• the inverse of the inverse of p ⇒ q is p ⇒ q

• the inverse of the the converse of p ⇒ q is ¬q ⇒ ¬p

• the inverse of the contrapositive of p ⇒ q is q ⇒ p

Other Questions
which major muscle group does the bench press and push-ups strengthen Identify the common difference of the sequence: 8, 1, 6, 13, Suppose In a Snap Ltd. Just issued a dividend of $1. 25 per share on its common stock. The company paid dividends of $. 85, $. 90, $1. 04, and $1. 10 per share in the last four years. If the stock currently sells for $45, what is your best estimate of the companys cost of equity capital using the arithmetic average growth rate in dividends? What if you use the geometric average growth rate?. Key Nutrients about Nutrition What do you know to be true about the values of p and q?09AM60503080 Lamar wants to replace a glass window in his restaurant. The window is in the shape of a square. Its side lengths are 11 feet. Suppose glass costs $5 for eachsquare foot. How much will the glass cost to replace the window?sax 5 ? Termina cada conversacin para indicar que la segunda persona est de acuerdo con la primera. 8. Carolina: A m no me gusta limpiar (to clean) la casa. Miguel: A m ____________________________. Immersive Reader(1 Point)tambientampoco WILL MARK BRAINLISTWhat is the solution to this system of equations?(I suggest using the elimination method by multiplying the first equation by 3.)2x + y = 206x - 5y = -4Points earned for putting your solution as an ordered pair. If work is shown, partial credit can be earned. The function f is defined below. f(x)=2x3 Find f(1). how is the atomic mass determined? 3. Luigi lives 10 miles from work and rides his fancy Segway there each day. He rides past oneblock every 45 seconds. Each block is 360 feet long. What is the rate, in feet per second atwhich Luigi rides his Segway?36 feet per secondB80 feet per second4.5 feet per secondD8 feet per second PLEASE ANSWER THIS QUICKGIVING BRAINLIEST TO THE ONE WHO ANSWERSRust is a compound that occurs when the element iron and oxygen combine. Do they create a physical or a chemical change? Which of the following best describes the advancements of the New Stone Age?a. using toolsusing seeds to grow cropsb. gathering foodusing fire to cook foodC.d.Please select the best answer from the choices provided BCD ^PLZ HELP, I NEED IT BY TODAY!!! (PART B and PART C only) PLZ THANKS What reasons can you give for why the North American French colonists put more effort into the fur trade than into farming? Karina uses the system of equations below to compare the monthly utility costs in July and December for electricity, x, and natural gas, y. 750x + 17y = 141.61 300x + 30y = 75.90 Karina solves the system using linear combination and arrives at the equation 116y = 96.28. She then solves this equation for y. Which statement explains Karinas solution? The cost of natural gas is $0.17 per unit. The cost of natural gas is $0.20 per unit. The cost of natural gas is $0.72 per unit. The cost of natural gas is $0.83 per unit. Tyler's brother WorksTyler's brother earns $12 per hour. The store offers him a raise-a 5% increase per hour.After the raise, how much will Tyler's brother make per hour? 1. Describe the equator and identify which letter represents it in the picture. Make sure to use a complete sentence in your response.BCSAVE & EXITSUBMIT ALL ANSWERS Using good judgment and making decisions are examples of which career skill?. Madelyn hikes 190.5 meters up amountain. If she is 62% of the wayup, how tall is the mountain? Roundto the nearest whole meter.