Prove that: (secA-cosec A) (1+cot A +tan A) =( sec^2A/cosecA)-(Cosec^2A/secA)

Answers

Answer 1

Step-by-step explanation:

[tex](\sec A - \csc A)(1 + \cot A + \tan A)[/tex]

[tex]=(\sec A - \csc A)\left(1 + \dfrac{\cos A}{\sin A} + \dfrac{\sin A}{\cos A} \right)[/tex]

[tex]=(\sec A - \csc A)\left(1 + \dfrac{\cos^2 A + \sin^2 A}{\sin A\cos A} \right)[/tex]

[tex]=(\sec A - \csc A)\left(\dfrac{1 + \sin A \cos A}{\sin A \cos A} \right)[/tex]

[tex]=\left(\dfrac{\frac{1}{\cos A} - \frac{1}{\sin A}+\sin A - \cos A}{\sin A\cos A}\right)[/tex]

[tex]=\dfrac{\sin A - \sin A \cos^2A - \cos A + \cos A\sin^2A}{(\sin A\cos A)^2}[/tex]

[tex]=\dfrac{\sin A(1 - \cos^2A) - \cos A (1 - \sin^2 A)}{(\sin A\cos A)^2}[/tex]

[tex]=\dfrac{\sin^3A - \cos^3A}{\sin^2A\cos^2A}[/tex]

[tex]=\dfrac{\sin A}{\cos^2A} - \dfrac{\cos A}{\sin^2A}[/tex]

[tex]=\left(\dfrac{1}{\cos A}\right)\left(\dfrac{\sin A}{1}\right) - \left(\dfrac{1}{\sin^2A}\right) \left(\dfrac{\cos A}{1}\right)[/tex]

[tex]=\sec^2A\csc A - \csc^2A\sec A[/tex]


Related Questions

Kayla made two paper chains. The paper links on one represented the number of days until her birthday, and the other showed the days until summer vacation. Altogether, she made 135 links for her chains. The birthday chain had twice as many links as the vacation chain. How many links are on Kayla's birthday chain?

Answers

Answer:

90 days

Step-by-step explanation:

b= number of days til  her birthday

s = number of days til summer

b+s =135

b = 2s

2s+s = 135

3s = 135

Divide by 3

3s/3 =135/3

s =45

b = 2s = 2(45) = 90

Please Help!!!


In the following expression, both A and B are variables that can take positive values.
A+2/B

Which of these actions will cause the expression's value to increase?
Choose 2 Answers
A.
Keeping A constant and increasing B

B.
Keeping A constant and decreasing B

C.
Increasing A and keeping B constant

D.
Decreasing A and keeping B constant

Answers

Answer:

B

kepping a constant and decreasing

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g Two different factories named A and B both produce an automobile part. If a part came from A, the probability that the part is defective is .04. If the part came from B, the probability that it is defective is .05. In a sample of 180 parts, 100 came from A and 80 came from B. (a) What is the probability that a part chosen at random (from the sample) was defective

Answers

Answer:

0.0444 = 4.44% probability that a part chosen at random (from the sample) was defective.

Step-by-step explanation:

Probability of a defective part:

0.04 of [tex]\frac{100}{180}[/tex], that is, coming from A.

0.05 of [tex]\frac{80}{180}[/tex], that is, coming from B. So

[tex]p = 0.04\frac{100}{180} + 0.05\frac{80}{180} = \frac{0.04*100 + 0.05*80}{180} = 0.0444[/tex]

0.0444 = 4.44% probability that a part chosen at random (from the sample) was defective.


Which line is horizontal?
O y=2
O y = 2x
O y = -2x
o y=x

Answers

Answer:

y=2

Step-by-step explanation:

A horizontal line has a slope of zero so the x term is zero

y = mx+b

y = b

y must equal a constant

X-3y=-3; ( ,4), (12, ) complete each ordered pair

Answers

Answer:

(9,4) and (12,5)

Step-by-step explanation:

x-3y=-3

y=4, x-3*4=-3, x=9. (9,4)x=12, 12-3y=-3, y=5. (12,5)

solve the following equations

Answers

Answer:

x=0,5/2

Step-by-step explanation:



Find two consecutive whole numbers that ✓39 lies between.

Answers

Answer:

6 and 7

Step-by-step explanation:

6^2 = 36 which is less than 39

7^2 = 49 which is more than 39

So the two numbers you want are

x = 6

y = 7

help help......................................................................................

Answers

Hey there! Is there more text to this? I would love to help, but there is no question.

five sutracted from x is at most -21 translate the sentence into an inequality?​

Answers

First of all, let’s look at the question. 5 subtracted from x. This means that it is 5 - x. Then, we know it is at most -21. That means that 5 - x needs to be less than or equal to -21.

Therefore, our equation is 5 - x < 21. Please note that the inequality sign should have a solid sign beneath.

The midpoint of AB is (1.2). The coordinates of A are (-3, 6) Find the coordinates of B.

Answers

Answer: coordinates of B are (5,-2)

Step-by-step explanation:

let B be (x2,y2)

x1 = -3 y1 = 6

x = 1

y = 2

so

x = (x2 + x1)/2

1 = (x2+(-3))/2

or, 2 = x2 - 3

so, x2 = 5

now

y = (y2+y1)/2

or, 2 = (y2 + 6)/2

or, 4 = y2 + 6

so, y2 = -2

Maybe you have considered buying a term life insurance policy. The expected value of any term life insurance product yields a positive expected value for the insurance company and a negative expected value for you, meaning the insurance company will make profits by selling their insurance products. Would you still buy the term life insurance? Why or why not? Are there other examples other than insurance that uses this same concept?

Answers

Answer:

Yes one should consider to buy the policy as important to have insured plan that help at the time of need.

Step-by-step explanation:

Term of life insurance is a form of life insurance which guarantees the payment of the stated death benefit. If the person des during the plan the term expires.  The policy has no value other than guarantee benefits. The term life insurance will make products by selling products and thus it's necessary to have insurance. Health, age, and life expectancy are some of the points that need to consider for buying plans.

look at the image below

Answers

Answer:

4.2 mi²

Step-by-step explanation:

Volume of a cone = (1/3)πr²h, where r = radius and h = height

(1/3)πr²h

= (1/3)×π×1²×4

= 4π/3

= 4.2 mi² (rounded to the nearest tenth)

8. Write 3x3 – 21x2 + 36x in factored form.
3x(x - 4)(x - 3)
3x(x - 5)(x - 2)
3x(x + 6)(x + 2)
O
3x(x + 4)(x + 3)

Answers

Answer:

A

Step-by-step explanation:

3x^3 – 21x^2 + 36x=3x(x^2-7x+12)=3x(x - 4)(x - 3)

is f(x)=e^-3x an exponential function?

Answers

Yes, because we have the number ‘e’ raised to x, although it is now -3x, it is still a variation of x

Volunteering: The General Social Survey asked 1309 people whether they performed any volunteer work during the past year. A total of 518 people said they did. Part: 0 / 30 of 3 Parts Complete Part 1 of 3 (a) Find a point estimate for the population proportion of people who performed volunteer work in the past year. Round the answer to at least three decimal places. The point estimate for the proportion of people who performed volunteer work in the past year is .

Answers

Answer:

The point estimate for the population proportion of people who performed volunteer work in the past year is 0.396.

Step-by-step explanation:

Point estimate of a proportion:

Proportion is the number of desired outcomes divided by the number of total outcomes.

518 out of 1309 people performed volunteer work:

This means that:

[tex]p = \frac{518}{1309} = 0.396[/tex]

The point estimate for the population proportion of people who performed volunteer work in the past year is 0.396.

I need help with this balance mobile please:)​

Answers

Answer:

blue 1

orange 5

green 3

I hope it is helpful and mark me as brainlest and follow me plz


A can of lemonade holds one-third of a litre. How many litres are there in 100 can

Answers

Answer:

33 Litres

Step-by-step explanation:

212.93 liters will be in 100 cans

If why varies with the square of x and Y equals 24 when x equals 10 then the constant of proportionality is ____, and the value of y when x equals 20 is ____. Assume x is greater than or equal to 0. Select two answers

Answers

Answer:

Step-by-step explanation:

y varies with the square of x:

y = kx²

y equals 24 when x equals 10

24 = k·10²

constant of proportionality k = 0.24

when x = 20, y = 0.24·20² = 96

"select two answers"  —where are the choices?

Let f(x)=x^3-6x+3 i. find the domain of the function and f’(x) in the domain.​

Answers

Domain of a any cubic function [tex]f(x)=ax^3+bx^2+cx+d[/tex] is defined to be always [tex]\mathbb{R}[/tex].

The derivative with respect to x of your cubic function is,

[tex]\dfrac{d}{dx}f(x)=f'(x)[/tex]

to find the derivative of a polynomial function, simply take a derivative of each factor and sum them up,

[tex]\dfrac{d}{dx}x^3=3x^2[/tex] by the rule [tex]\dfrac{d}{dx}x^m=mx^{m-1}[/tex] where [tex]m\in\mathbb{R}[/tex]

[tex]\dfrac{d}{dx}-6x=-6[/tex]

[tex]\dfrac{d}{dx}3=0[/tex]

So the derivative is,

[tex]f'(x)=3x^2-6[/tex]

both derivative and the original function have equal domain.

Hope this helps :)

Step-by-step explanation:

[tex]thank \: you[/tex]

What is the mapping for a reflection in the line y=-1

Answers

Answer:

0

Step-by-step explanation:

the key mapping for a reflection in the line y=-1 is 0

write 342 to 1 significant figure​

Answers

Answer:

300

Step-by-step explanation:

A significant figure is the most important (largest) number you can round it to.

As it wants 1 significant figure, you count 1 to the left and round the 4 down.

Hope this helps :)

Hey there, everyone!

I just wanted to shout out to all of those whom have helped me through my tortuous math homework and say thank you very much. XD

I manage to pass my very first year of high school without physically going to school.

It was a lot of twist and turns, I must say. But at least I managed to pass through!

Man, I'm gonna miss 2021 because now I'll have to ACTUALLY go to school. But when that day comes, I do hope you guys will continue helping me on!

In the mean time, stay safe everyone and thanks a lot!

But hold up! I got one more question!

I really want to delete my account so badly but I can't because I forgot my password and I'm using my school email unfortunately. Anyone got a solution to my issue? :(

Answers

Answer:

I don't know the answer please tell me

Bà B đến ngân hàng ngày 05/05/2019 để gửi tiết kiệm 250 triệu đồng thời hạn 3 tháng, lãi suất 7%/năm, NH trả lãi định kỳ hàng tháng (kỳ lĩnh lãi đầu tiên là ngày 05/05/2019). Đến ngày 05/08/2019, bà B tất toán sổ tiết kiệm trên. Tính số tiền bà B nhận được vào ngày đáo hạn sổ tiết kiệm là? (Cơ sở công bố lãi suất là 365 ngày)

Answers

Answer:

Ask in English then I can help u

Answer the picture. X=450 BAC= 82 ABC=52
What’s the distance between A to C

Answers

Answer:

Hello,

Step-by-step explanation:

[tex]mes\ \widehat{C}=180^o-82^o - 52^o=46^o\\\\Using\ law\ of\ sinus:\\\dfrac{AB}{sin(C)}= \dfrac{AC}{sin(B)} \\\\\dfrac{450}{sin(46^o)}= \dfrac{AC}{sin(52^o)} \\\\AC=\dfrac{450*sin(52^o)}{sin(46^o)}= 492.9587..(ft)\approx{493(ft)}[/tex]

Find the missing Side of the triangle

Answers

Answer:

2√15

Step-by-step explanation:

Use the Pythagorean theorem.

2² + x² = 8²

x² + 4 = 64

x² = 60

x² = 4 * 15

x = 2√15

tentukan himpinan penyelasaian dari plsv berikut. A:3x+=2x+12​

Answers

Answer:

x=12

Step-by-step explanation:

3x=2x+12

3x-2x=12

x=12

The perimeter of Tamara's suitcase is 8x - 3 and the perimeter of Anna's suitcase is
3x + 2. Write an algebraic expression that represents
the difference between the perimeter of Tamara's suitcase
and the perimeter of Anna's suitcase?

Answers

Answer:

perimeter: 2

Step-by-step explanation:

8x-3 = 6x

8x – 6x = 3

2x = 3

x = 3/2

The required algebraic expression that represents the difference between the perimeter of Tamara's suitcase and the perimeter of Anna's suitcase is 5x - 5.

What are equation models?

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
The difference between the perimeter of Tamara's suitcase and Anna's suitcase can be found by subtracting the expression for the perimeter of Anna's suitcase from the expression for the perimeter of Tamara's suitcase:

(8x - 3) - (3x + 2)

Simplifying the expression by removing the parentheses and combining like terms, we get:

8x - 3 - 3x - 2

= 5x - 5

Therefore, the algebraic expression that represents the difference between the perimeter of Tamara's suitcase and the perimeter of Anna's suitcase is 5x - 5.

Learn more about models here:
https://brainly.com/question/22591166
#SPJ7

Find the zeros of the function in the interval (-2 pie, 2 pie). f(x) = 3 cos x

Answers

Answer:

Roots are -π/2 and π/2

Step-by-step explanation:

[tex]{ \bf{f(x) = 3 \cos(x) }}[/tex]

when x is -2π:

[tex]{ \sf{f( - 2\pi) = 3 \cos( - 2\pi) }} \\ { \sf{ = 3}}[/tex]

hence -2π is not a zero of the function

when x is 2π:

[tex]{ \sf{f(2\pi) = 3 \cos(2\pi) }} \\ { \sf{ = 3}}[/tex]

hence 2π is not a zero of the function

when x is π/2:

[tex]{ \sf{f( \frac{\pi}{2}) = 3 \cos( \frac{\pi}{2} ) }} \\ { \sf{ = 0}}[/tex]

Hence ±π/2 is the zero of the function.

The prices of paperbacks sold at a used bookstore are approximately Normally distributed, with a mean of $7.85 and a standard deviation of $1.25.


Use the z-table to answer the question.


If the probability that Joel randomly selects a book in the D dollars or less range is 56%, what is the value of D?


$4.46

$7.75

$8.04

$8.10

(C) 8.04

Answers

Answer:

The answer you want is indeed, (C).

8.04

ED2021

Answer:

C) 8.04

Step-by-step explanation:

edge 2023

Find the mean for the amounts: $17.482: $14.987: $13.587$14.500, $18.580. $14.993​

Answers

Answer:

The mean of these numbers is 15.68816 with a repeating 6.

Step-by-step explanation:

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