Mathematics High School

prove that: (sinθ/1+cosθ) + (1+cosθ/sinθ) = 2cosecθ
[tex] \: prove \: that: \frac{ sinθ}{1+cosθ}+ \frac{1+cosθ}{sinθ} = 2 \: cosec \: θ [/tex]
​

Answers

Answer 1

Consider LHS

(sinθ/1+cosθ) + (1+cosθ/sinθ) =

= [sinθ(sinθ)+(1+cosθ)+(1+cosθ)]/[(1+cosθ)(sinθ)]

= [sin²θ+(1+cosθ)²]/[(1+cosθ)sinθ]

= [sin²θ+1+cos²θ+2cosθ]/[(1+cosθ)sinθ]

[°.° (a+b)² = a²+2ab+b²]

Here, a = 1, b = cosθ

= [(sin²θ+cos²θ)+1+2cosθ]/[(1+cosθ)sinθ]

= [1+1+2cosθ]/[(1+cosθ)sinθ]

[°.° sin²θ+cos²θ = 1]

= [2+2cosθ]/[1+cosθ)sinθ]

= [2(1+cosθ)]/[(1+cosθ)sinθ]

= 2/(sinθ)

[°.° 2/sinθ = cosecθ]

= 2cosecθ = RHS.

Hence, Proved.

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Related Questions

If triangle he an area of 36 and a height of 12 calculate the length of the base.

Answers

Answer:

Below.

Step-by-step explanation:

A = 1/2bh for a triangle.

36 = 1/2b(12)

36 = 6b

----    ----

6        6

b = 6

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Answers

Answer:

D

Step-by-step explanation:

I think it might be (D) $2x-5

Tracy has 3/4 pounds of rice to give to 6 of her friends. If each
friends gets an equal amount, how much rice will each friend
receive?

Answers

Answer:

1/8 Pounds

Step-by-step explanation:

Since Tracy gives 3/4 pounds of rice to 6 of her friends, you will need to divide it among 6 people.

3/4 ÷ 6

= 3/4 * 1/6

= 1/4 * 1/2 (cross multiplication)

= 1/8.

Therefore, each of her 6 friends received 1/8 Pounds of rice

I hope this helped!

what is equivalent to |14-20|

Answers

Answer:

7/10

Step-by-step explanation:

Byron did 80% of the assignments this quarter. If he had a total of 20 assignments, how many did he do?



HELP ASAP I NEED IT BY 4:00 PLS HELPPPPPPPPPPPP

Answers

Answer:

5/20

quater is divided into 4 pieces to get a whole and 3/4 is 15 and 1/2 is 10 and 20 is whole and 1/4 is 5

Rafael has two coupons for a phone.

Coupon A:

Coupon B:

$8 rebate on a $57 phone

20% off of a $57 phone

Choose the coupor that gives the lower price.

Then fill in the blank with the correct value.

Coupon A gives the lower price.

The price with coupon A is $] less than the price with coupon B.

Coupon B gives the lower price.

The price with coupon B is $] less than the price with coupon A.

lol

Answers

Coupon B would give the lower price because 20% off 57 is 45.60 and 8 dollars off 57 is 49

plz help will mark as brainliest​

Answers

Answer:

Side AB and side BC

Step-by-step explanation:

Hope it helps


[tex]\{ x - ( \frac { x } { 5 } + 60 ) \} = \{ ( \frac { 4 } { 5 } ) x - 60 \}[/tex]
help plssssssss
​

Answers

If you are asking for the value of x, then x = not defined because dividing a value by 0 will always give you a non-defined answer. So, x can be equal to any number (there can be infinite values).

Next, if you want to prove that both the statements are true, then yes it's true because RHS = LHS = 0.

Check the 2 attachments for the steps.

______

RainbowSalt2222 ☔

Answer:

infinite number of solutions

Step-by-step explanation:

x - ([tex]\frac{x}{5}[/tex] + 60) = [tex]\frac{4}{5}[/tex] x - 60 ← distribute parenthesis on left by - 1

x - [tex]\frac{x}{5}[/tex] - 60 = [tex]\frac{4}{5}[/tex] x - 60 , collect like terms on left side

[tex]\frac{4}{5}[/tex] x - 60 = [tex]\frac{4}{5}[/tex] x - 60

Since expressions on both sides are equal then any value of x is a solution.

That is there is an infinite number of solutions

um I need help with thissss

Answers

Answer:

its you again

Step-by-step explanation:

if they have the same amount of dashes on the same sided they are congruent

does that answer your question

if they have the same amount of dashes on the same sided they are congruent

Does anybody like anime ??

Answers

of course bro why wouldn’t we like anime

Please Help Me :) I'm giving brainliest to correct answers only and No LiNkS.

Answers

Answer:

c

Step-by-step explanation:

it makes the most sense

The correct answer to this question is C! The first plot point explains how it starts the line and progresses through intervals of 50 each year after. Hope that helps!

Steve increases his math average by 9 points over a period of 15 weeks. How many points per week did his average increase?

Answers

Answer:

.6 points per week

Step-by-step explanation:

9/15

What is an equation of the following line?

Answers

Answer:

y = 5

Step-by-step explanation:

The equation of a horizontal line parallel to the x- axis is

y = c

where c is the value of the y- coordinates the line passes through.

The line passes through all points with a y- coordinate of 5 , then

y = 5 ← equation of line


Use the ALEKS calculator to write9/16
as a decimal rounded to the nearest hundredth.

Answers

9/16 = .5625

Rounding to the nearest hundredth, the answer is .56

Name the congruent triangles.

Answers

Answer:

ΔOGD≅ ΔPRC

Step-by-step explanation:

Alyssa fed her dog 2/3 cup of dog food in the morning and another 5/8 cup in the evening. How much did her dog eat over the course of the day? Write your answer as a mixed number​

Answers

1 7/24 is the correct answer I will show you how to get it if needed.

Answer:

1  7/24

Step-by-step explanation:

2/3 x 8/8= 16/24

5/8 x 3/3= 15/24

31/24 = 1 7/24

a÷b when a = 2 and b = 1/2

Answers

Answer:

4

Step-by-step explanation:

a ÷ b = 2 ÷ 1/2 = 2 × 2/1 = 4

A rectangular field is four times as long as it is wide. If the perimeter of the field is 410 yards, what are the​ field's dimensions?

Answers

The length of the rectangular field is 164 yards and the width is 41 yards

From the question,

We are to determine the fields dimensions

From the given information

A rectangular field is four times as long as it is wide

That is

l = 4w -------- (1)

The perimeter of a rectangle is given by

P = 2(l + w)

Where

P is the perimeter

l is the length

and w is the width

From the given information

The perimeter of the field is 410 yards

∴ 2(l + w) = 410 ------ (2)

Substitute equation (1) into equation (2)

2(4w + w) = 410

2(5w) = 410

10w = 410

∴  w = 410 ÷ 10

w = 41 yards

Substitute the value of w into equation (1)

l = 4(41)

l = 164 yards

Hence, the length of the rectangular field is 164 yards and the width is 41 yards.

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Choose the steeper line.
y=1/2x-3
or
y=1/4x -8

Answers

Hello there!

y=1/2x-3 is steeper than y=1/4x-8

The bigger the slope, the steeper the line.

Hope this helps!

~Just a cheerful teen

#CarryOnLearning

[tex]SilentNature[/tex] here to help

1 + tan^2 (π/6) = _______.


A. csc^2 (π/6)

B. sec^2 (π/6)

C. cot^2 (π/6)

D. 1 - tan^2 (π/6)

Answers

Answer: B??

Step-by-step explanation:

Correc me if i wrong ovo

Find the slope of the line containing the points (-3,-4) and (7,-6).

Answers

Answer:

-1/5

Step-by-step explanation:

slope formula

David drove 236 miles in 4 hours. On average, how fast did he drive, in miles per hour?

Answers

Answer:

59 mph

Step-by-step explanation:

236/4 = 59

Steps:

1. State the question: 236 miles in 4 hours

2. Now convert the question to equation: 236 miles/4 hours = question miles/hour

3. Divide: 59 miles/hour or 59 miles per hour

I WILL GIVE BRAINLIEST PLSSSSSSSSSSS

The area of a rectangle is 3/4 square yards. If the width of the rectangle is 3/5, what is the length?
EXPRESSION :
ANSWER:

Answers

I think that the answer is 1.25

Answer:

L = 5/4 yards

L = 1 1/4 yards

L = 1.25 yards

Step-by-step explanation:

area = Length * Width

3/4 = L * 3/5

Divide both sides by 3/5

(3/4) / (3/5) = L

When dividing by a fraction flip it over and multiply

3/4 * 5/3 = L

The 3 cancels

5/4 = L

L = 5/4 yards

as a proper fraction

L = 1 1/4 yards

As a decimal

L = 1.25 yards

Find the value of x in the equation below. 15.4=x-13.9

Answers

Answer:

29.3

Step-by-step explanation:

How would you write 262 × 3 in addition form?
600 + 18 + 6
600 + 180 + 6
618 + 6
600 + 180 + 6 × 3

Answers

Answer:

262x3=768 so you need to find which answer equals 786 in addition form.

option a is equal to 624

option b is equal to 786

option c is equal to 624

option d is equal to 2358

your answer would be option b.

Step-by-step explanation:

hope this helps

f(x) = 2(x − 2)2 + 3

Answers

Answer:

4x-5

Step-by-step explanation:

the answer is 4x-5 as we apply multiplication and subtraction

3.) What would 9 gallons of gas cost at $2.12 per gallon? *
$18.80
O $17.56
$19.08
$11.12

Answers

Answer:

19.08

Step-by-step explanation:

each gal = $2.12

gals filled = 9

9 x 2.12 = 19.08

Name three integers between −12 and −7. And no bots allowed.

Answers

Answer:

-11 -10 -9

Step-by-step explanation:

I'm not 100% sure

Answer:

-10 , -9 , -8

Step-by-step explanation:

An Integer is a whole number, regardless of the sign (positive or negative).

In this case, the numbers between -12 and -7 are:

-11 , -10 , -9 , -8

So you can decide which 3 integers you want.

~

Marco is making a kite, using sticks for its diagonals. One stick is 2 feet long and the other is 3 feet long. How much material will Marco need to make the kite? 2 square feet 3 square feet 4 square feet 6 square feet.

Answers

Answer:

3 square feet

Step-by-step explanation:

Got it right because of the answer above :)

Marco will need 3 square feet of material to make the kite.

What is an expression?

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

We can use the formula for the area of a kite, which is:

A = (1/2) x d1 x d2

where d1 and d2 are the lengths of the two diagonals.

In this case,

d1 = 2 feet, and d2 = 3 feet.

Substituting these values into the formula, we get:

A = (1/2) x 2 feet x 3 feet

   = 3 square feet

Therefore,

Marco will need 3 square feet of material to make the kite.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ7

At the local deli, David bought two ginger ales and two bagels for $6.60. Sumaiya bought four ginger ales and three bagels for $11.70.

Find the exact cost of one bagel and one ginger ale.


PLS HELP

Answers

Step-by-step explanation:

let the ginger ales be $x and the bagels $y.

Case 1, 2x+2y=6.60 x+y=3.30 ......1

Case 2, 4x+3y=11.70. .....2

1, x+y=3.30...×4

2, 4x+3y=11.70...×1

1, 4x+4y=13.20

2, 4x+3y=11.70

(-) (-) (-)

____________

y=1.50

____________

now, placing the value of y in equation 1,

x+y=3.30

x+1.50=3.30

x=1.80

therefore, the exact cost of one bagel and one ginger ale is $1.50 and $1.80 respectively.

hope this helps you.

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