1)cot a/2 -tan a/2 = 2 cot a
2) cot b/2 + tan b/2= 2 cosec b
prove​

Answers

Answer 1
1)

LHS = cot(a/2) - tan(a/2)

= (1 - tan^2(a/2))/tan(a/2)

= (2-sec^2(a/2))/tan(a/2)

= 2cot(a/2) - cosec(a/2)sec(a/2)

= 2(1+cos(a))/sin(a) - 1/(cos(a/2)sin(a/2))

= 2 (1+cos(a))/sin(a) - 2/sin(a)) (product to sums)

= 2[(1+cos(a) -1)/sin(a)]

=2cot a

= RHS

2.

LHS = cot(b/2) + tan(b/2)

= [1 + tan^2(b/2)]/tan(b/2)

= sec^2(b/2)/tan(b/2)

= 1/sin(b/2)cos(b/2)

using product to sums

= 2/sin(b)

= 2cosec(b)

= RHS

Related Questions

Solve the system of equations. If the system has no solution, say that it is inconsistent. Graph the lines of the system.
x + y = 7
x - y = 5
Select the correct choice below and, if necessary, fill in any answer boxes within your choice.
A. The solution is x= 6 and y = 1. (Type integers or simplified fractions.)


** i know that x=6 and Y=1. I don’t know how to graph it. It gives me a hint that the lines need to be in slope intercept form but again, I dont know how to graph! **

Answers

So the easiest way would be to change them into slope intercept form

x + y = 7

y = - x + 7

x - y = 5

y = x - 5

The coefficient of x is the slope, since none of them have a coefficient, their slopes are 1. The first line has negative x which means the slope is negative one, which you can draw from top left to bottom right and a positive slope is drawn from top right to bottom left.

The number after x is the y-intercept which is where the line intercepts the y-axis.

To draw, put a dot on the y-intercept and with a slope of one, go up and right one, or the opposite which is go down one and left one and put another dot and draw a line between the two dots. With a slope of negative one, go up one and go left one, or the opposite which is go down one and right one and draw a line between the two dots.

Customers at a gym pay a membership fee to join and then a fee for each class they attend. Here is a graph that represents the scenario.

What is the slope of the line?

Answers

where is the graph ? i can help

Please helpp!! best answer gets brainliest​

Answers

Answer:

the answer is B and C, because B equals .57 and C is .666 continuous

Answer:

C

Step-by-step explanation:

Turn everything into a fraction (round if needed)

4/7 = 0.571

A. 2/5 = 0.4 (0.4 < 0.57) since 0.4 is smaller than 0.57, it’s not A.

B. 0.57 (0.57 < 0.571) 0.56 is less than 0.571, so the answer could not be B.

C. 2/3 = 0.67 (0.67 > 0.57) 0.67 is greater than 0.571, meaning the answer could be C.

The triangles shown below must be congruent.
25°
55-7
100"
100
55"
25°
0
о
A. True
о
B. False

Answers

9514 1404 393

Answer:

  B.  False

Step-by-step explanation:

The three pairs of corresponding angles have the same measures, so the triangles are similar by AA similarity. However, at least one pair of corresponding sides must be shown congruent before the triangles can be declared congruent.

There is nothing in the diagram to require the triangles be congruent.

With three corresponding equal angles triangles are not congruent. Therefore, the given statement is false.

What is the congruence theorem?

Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.

The three pairs of corresponding angles have the same measures, so the triangles are similar by AA similarity. However, at least one pair of corresponding sides must be shown congruent before the triangles can be declared congruent.

With three corresponding equal angles triangles are not congruent. Therefore, the given statement is false.

To learn more about the congruent theorem visit:

https://brainly.com/question/24033497.

#SPJ7

Find the value of e.

Answers

Step-by-step explanation:

sum of three angles in a triangle is 180

55+35+x=180

90+x=180

x=180-90

x=90

hen Max was a puppy, he weighed 512 pounds. At his 1-year check-up with the vet, Max weighed 15.8 pounds.

How much weight did Max gain between the time he was a puppy and his 1-year check-up?

Enter your answer as a decimal or simplified mixed number in the box.

Answers

Answer:

10.3lbs or 10 3/10 as a mixed number

Step-by-step explanation:

i have the same question on my test so i know this is right but here's an explanation: so 5 1/2 pounds is the same as 5.5 pounds, and if you add 10 pounds to 5.5 pounds, you get 15.5 pounds, which is 3 ounces away from 15.8 pounds. so adding 3 ounces to the 10 pounds, then adding that to the 5.5 pounds, you would get 15.8. therefore, your answer is 10.3lbs.

The puppy gained 10.3 pounds of weight in 1 year.

What is subtraction?

Subtraction is one of the arithmetical operations, to subtract means to take away from a group or a number of things.

Given that, Max was a puppy, he weighed [tex]5\frac{1}{2}[/tex] pounds. At his 1-year check-up with the vet, Max weighed 15.8 pounds.

[tex]5\frac{1}{2}[/tex] pounds = 5.5 pounds

Weight before 1 year = 5.5 pounds

Weight after 1 year = 15.8 pounds

Weight gained by the puppy in 1 year = 15.8-5.5 = 10.3 pounds

Hence, the puppy gained 10.3 pounds.

For more references on subtraction, click;

https://brainly.com/question/2346316

#SPJ2

in an auditorium,there are 104 rows with 24 seats in each row.how many seats are available?

Answers

Answer:

2,496 seats

Step-by-step explanation:

If there are 104 rows with 24 seats in EACH row, we must multiply to find the answer. Which is gives you the equation: 104 x 24 = 2,496

hope this helps!

mark me brainliest :D

Simplify to the form of a square root of b

Answers

Answer:

If we substitute a and b to equal 6 for example

it would be

6

2

+

6

2

it would equal 8.5(1.d.p) as it would be written as

36

+

36

giving a standard form as

72

However if it was

6

2

+

6

2

it would equal 12 as the

and

^

2

would cancel out to give the equation 6+6

Therefore

a

2

+

b

2

cannot be simplified unless given a substitution for a and b.

I hope this isn't too confusing.

Step-by-step explanation:

2 pts
Sammy wants to buy a new stereo priced at $439. He enters into an agreement to pay
$22 a month for 24 months. How much will the finance charge be for this purchase?
State your answer in terms of dollars rounded to the nearest cent (hundredth).

Answers

Answer:

$308

Step-by-step explanation:

I am not sure if this is correct. But try it and let me know if it was

Any hot topic online promo codes???​

Answers

try YAY50, brainliest?

Help help help help help

Answers

Answer:

x>22

Step-by-step explanation:

3(x+4)>18

3x+12> 54

3x>66

x>22

I need help with part a and b please

Answers

Answer:

The total answer should be 38 on the top

Step-by-step explanation:

a) So the first partial quotient would be equal to 30 as 31 x 30 = 930

b) Second partial quotient would be 8 as 31 x 8 = 248

Answer:

0

38

I hope it's help byeeee

Where do I put the parenthesis to make it true?

5 – 6w – 5 – 95 + 2w = –48w – 70

Answers

Answer:

i just stole your points thank you

Step-by-step explanation:

5 – 6w – 5 – 95 + 2w = –48w – 70

-6w + 2w + 48w = -70 -5 + 5 +95

44w = 25

w=25/44

An airplane starts to descend from an altitude over 30,000 feet at what rate is the airplane descending?

Answers

Answer:

20,000 feet

Step-by-step explanation:

Based on the initial altitude and the rate that the plane is descending, the relevant equation is = 30,000 - 2,000x. The altitude after 5 minutes is 20,000 feet above sea level.

The plane begins at 30,000 feet above ground and is descending at 2,000 feet per minute. The relevant equation after x minutes is:

= Initial altitude - (Descent in feet per minute x Number of minutes)

Plugging in the values gives:

= 30,000 - (2,000 × x)

= 30,000 - 2,000x

creds to Parrain

3x+2=198
Solve it as Soon as possible!​

Answers

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

Let's solve for x ~

[tex]3x + 2 = 198[/tex]

[tex]3x = 198 - 2[/tex]

[tex]3x = 196[/tex]

[tex] \boxed{ \boxed{x = \dfrac{196}{3} } \: \: or \: \: \boxed{ x = 65.33}}[/tex]

Answer:

[tex]\boxed{\blue{ = \frac{196}{3}}} [/tex]

Step-by-step explanation:

Let's solve your equation step-by-step.

3x+2=198

Step 1: Subtract 2 from both sides.

3x+2−2=198−2

3x=196

Step 2: Divide both sides by 3.

[tex] \tt \: \frac{3x}{3} = \frac{196}{3} [/tex]

Result:

[tex]\boxed{\underline{ x = \frac{196}{3}}} [/tex]

if a shirt is 50$ and is on sale for 20% off how much wil you pay with 6% sales tax

Answers

Answer:

42.4 is the correct answer to this question

The governor of state A earns $51,615 more than the governor of state B. If the total of their salaries is $291,335, find the salaries of each.

Answers

Answer:

A = $171,475, B = $119,860

Step-by-step explanation:

A represents the salary of the governor of state A.

B represents the salary of the governor of state B.

A is $51615 larger than B, so you get the equation:

A = B + 51615

The total of the two salaries is $291335, so you can the second equation:

A + B = 291335

Using the first equation, substitute the quantity (B + 51615) for A in the second equation.

(B + 51615) + B = 291335

2B + 51615 = 291335

2B = 239720

B = 119860

Plug this value of B back into either of the equations.

A = B + 51615 = 119860 + 51615 = 171475

Please answer
A=
B=
C=

Answers

Answer:

I can't see the file

Step-by-step explanation:

Which of the following is a solution of y - x < -3?

(6, 2)
(2, 6)
(2, -1)

Answers

Answer:

2,-1

Step-by-step explanation:

What is the answer for 14.05 x 7

Answers

the answer is 98.35.

Answer:

98.35

there that is the answer

help pls and ty! i will give brainliest to the correct answer

Answers

Answer: 24km

Step-by-step explanation:

given 1cm : 8km

distance between cafe and restaurant upply store= 3cm

Real distance = 3x8 =24 km

Which of these angle pairs are congruent because they are corresponding
angles?


A. 2 and 4
B. 2 and 3
C. 2 and 5
D. 2 and 6
SUBMIT

Answers

It’s c bc I took the test

Answer: it’s 2 and 6

Step-by-step explanation:

14. Explain why a rotation of positive 180 degrees is the same as a rotation of -180 degrees.​

Answers

Answer:

t is the same because...

Step-by-step explanation:

turning -180 is like turning right turning left no matter how you turn you will still be in the opposite from which you started

Xavier is going to use a computer at an internet cafe. The cafe charges an initial fee to use the computer and then an additional price per minute of usage. Let C represent the total cost of using a computer for t minutes at the internet cafe. A graph of C is shown below. Write an equation for C then state the slope of the graph and determine its interpretation in the context of the problem.

C = ???
The slope of the function is ? which represents:
A: The total charge of using a computer
B: The number of minutes the computer was used
C: The additional charge per minute
D: The initial charge to use a computer

Answers

Answer:

  C = 1/5t +6

  slope: 1/5, (C) The additional charge per minute

Step-by-step explanation:

Before we can write the function, we need to know the slope of the line. Marked points are separated by 5 units horizontally (run=5) and 1 unit vertically (rise=1). The slope is ...

  m = rise/run = 1/5

The initial charge is the C-intercept: 6. The function can be written in slope-intercept form as ...

  C = 1/5t +6

__

As we saw above, the slope of the function is 1/5, which represents ...

  the additional charge per minute

There are about 3 × 1020 gallons of salt water on the earth, while there are about 6 × 1018 gallons of fresh water. About how many times the amount of fresh water is the amount of salt water? 200 times the amount 500 times the amount 2 times the amount 50 times the amount

Answers

Answer C

Step-by-step explanation:

I can use structure to decide where to place the first digit in a quotient. A strongly agree B. agree C. disagree qD. strongly disagree​

Answers

Answer: For this question, it's just like a self-survey. If you understand this concept strongly or not really, you go with that answer like strongly agree, agree, etc.

If a line has the x-intercept of (4,0) and no y-intercept, what is the Slope-intercept form equation ? Please !!

Answers

Answer:

y=mx+c

0=m(4)+c

c=4m

positive slope

guys help me with this question

Answers

Blank 1: 7

Blank 2: 3

Blank 3: 2

Blank 4: 2

Help I have a C in math. I don't understand this Alegbra. If you get it right then I will give you Brainlist!​

I know I already got the right answer so please give an explanation too!​​

Answers

Answer:

11

Step-by-step explanation:

to find the area of a square: base times height, we know that all sides of a square are the same. So, 11*11

=121, the answer is 11

Answer:

11 in.

Step-by-step explanation:

The canvas has the shape of a square.

The area of a square is the side times the side, but since in a square, all sides have equal lengths, then the area of a square is the square of the side.

You are given the area. You need to find the side.

The area is the square of the side, so the side is the square root of the area.

side = √area

side = √(121 in.²)

side = 11 in.

(3)a train travel 252 km in 42 hours. what amount of time will it take to complete a journey of 350km. (4) calculate the cost of 15 article at $1.95 each cost. (5) if 25 article cost 43.75 how much does each cost. (6) A car travel 240km on 20 liter of petrol. how many liters of petrol is needed to travel 600km​

Answers

Answer:

(3)

Distance the train can travel=252km

Distance the train can travel in 1 hour=252÷42=6km

The time needed to cover 350km= 350÷6=58.4 hours.

(4)

The cost of 1 articles=$1.95

The cost of 15 articles= 15(1.95)=$29.25

(5)

Cost of 25 articles= 43.75

Cost of 1 article= 43.75/25=1.75

(6)

Liters of petrol needed when a car travels 240km=20litre

liters of petrol needed when a car travels 600km= 20/240 x600

20/24x60

20/4x10

5x10=50liter

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