How do I verify: tan(x)+cot(x)=(2)/sin(2x)?

I always get stuck after writing out (sin^2x+cos^2x)/sin(x)cos(x)

Answers

Answer 1

[tex]sin^2(\theta)+cos^2(\theta)=1\qquad \qquad sin(2\theta)=2sin(\theta)cos(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]tan(x)+cot(x)=\cfrac{2}{sin(2x)} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{doing the left-hand-side}}{\cfrac{sin(x)}{cos(x)}+\cfrac{cos(x)}{sin(x)}\implies \cfrac{sin^2(x)+cos^2(x)}{\underset{\textit{using this LCD}}{sin(x)cos(x)}}} \implies \cfrac{1}{sin(x)cos(x)}[/tex]

now, let's recall that anything times 1 is just itself, namely 5*1 =5, 1,000,000 * 1 = 1,000,000, "meow" * 1 = "meow" and so on, so we can write anything as time 1.

let's recall something else, that same/same = 1, so

[tex]\cfrac{cheese}{cheese}\implies \cfrac{spaghetti}{spaghetti}\implies \cfrac{horse}{horse}\implies \cfrac{butter}{butter}\implies \cfrac{25^7}{25^7}=1[/tex]

therefore

[tex]\cfrac{1}{sin(x)cos(x)}\cdot \cfrac{2}{2}\implies \cfrac{2}{2sin(x)cos(x)}\implies \cfrac{2}{sin(2x)}[/tex]


Related Questions

please need help with this Calculus question

Answers

So what’s the question?

The radius of the circle shown below is 8 centimeters. What is the
approximate length of XY?
115

A. 50.3 cm
B. 16.1 cm
C. 8.0 cm
D. 64.2 cm

Answers

16.1 cm! correct if wrong!

The angle of depression from a window 10 m above the ground to a coin on the ground is 15°. Find the distance of the coin from the base of the building. Show your reasoning for each step.

Answers

Here is the answer and the working

(fog) f(x) = 1/x g(x) square root x+3

Answers

Answer:

see the step below, but I'm not sure if this you want

Step-by-step explanation:

[tex](fog) = \frac{1}{ \sqrt{x + 3} } [/tex]

[tex](fog) = \frac{ \sqrt{ x + 3} }{x + 3} [/tex]

If the sum of six consecutive even integers is 438, what is the smallest of the six integers?

Answers

46
Because the sum of six consecutive is 46

what is 12 3/4 divided by 3

Answers

Answer:

4.25 as decimal and 4 1/4 as a fraction

Step-by-step explanation:

There are two types of packages that are available for hotel stay

- you can use the hotel unlimited for $500 a month

- Or you can spend $50 a day per visit.

Enter an equation that can be used to find the number of visits per month needed for the two packages to cost the same amount

Answers

Answer:

for one month 500$

for daily visit 50$

500$=50$*x days

x days=500$/50$

x days = 10 days

10 days of daily visits costs 500$ equal to one month

Can someone help me with these 2 geometry questions?? Will mark brainiest :)

Answers

Answer:

Thats to hard Do it your self

Please hurry!! This assignment is almost due thank you!!

Answers

Answer:

x = 33

Step-by-step explanation:

(x-17)°+(5x-1)°=180°

6x-18 = 180

6x = 198

x = 33

Emily reads a story book. o the first day, she reads 1/9 of the whole book, and on the second day, she reads 24 pages. The ratio of the number of pages read to the remaining pages in the two days is 1:4. How many pages are there in this book

Answers

Answer:

Step-by-step explanation:

Let P be the number of pages

First day reads P/9 pages

Second day reads 24 pages

two days reading is P/5  (1 page read for every 4 pages left)

         P/9 + 24 = P/5

        P + 24(9) = 9P/5

  5P + 24(9)(5) = 9P

               1080 = 4P

                     P = 270 pages

There are 270 pages in this book.

Given that,

Emily reads a storybook the first day,

She reads 1/9 of the whole book, and on the second day, she reads 24 pages.

The ratio of the number of pages read to the remaining pages in the two days is 1:4.

We have to find

How many pages are there in this book?

According to the question,

Let, P is the number of pages,

The first day Emily reads p/9 pages of the whole book,

And the second day she read 24 pages.

The ratio of the number of pages read to the remaining pages in the two days = 1;4 = p/5.

Therefore,

The number of pages reads first day + the number of pages read the second day = The ratio of the number of pages read to the remaining pages in the two days

[tex]\rm \dfrac{p}{9} + 24 = \dfrac{p}{5}\\\\ \dfrac{p}{5} - \dfrac{p}{9} = 24\\\\\dfrac{p \times 9 - p\times 5}{45} = 24\\\\ \dfrac{9p-5p}{45} = 24\\\\\dfrac{4p}{45} = 24\\\\4p = 24\times 45\\\\4p = 1080\\\\p = \dfrac{1080}{4}\\\\p = 270 \ pages[/tex]

Hence, there are 270 pages in this book.

For more details refer to the link given below.

https://brainly.com/question/14505922

Please help me!! I don't understand
No linksssss

Answers

Answer:

thanks haahhahahaha

Step-by-step explanation:

Oceanside Bike Rental Shop charges 13 dollars plus 8 dollars an hour for renting a bike. Tim paid 45 dollars to rent a bike. How many hours did he pay to have the bike checked out?​

Answers

Step-by-step explanation:

Shop charges =13

Many left for renting bike = 45-13 =$32

If renting for 1hr cost $8

then renting for X Hrs will cost $32

1/X =8/32 cross multiplying

8X= 32

X= 32÷8= 4hrs

A square is a quadrilateral with four equal sides and four 90 degree angles. Is quadrilateral ABCD a square?

Answers

Answer: yes

Step-by-step explanation:

need this soon please

Answers

Answer: pretty sure -7

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

(-80) - (-10) is -79

-70 / (+10) = -7

PLEASE HELP!!!! Identify the mistake and use the correct answer to the problem!!!

Answers

Answer:

1 [tex]\frac{3}{8}[/tex]

Step-by-step explanation:

the denominators must be the same so, since 4 goes evenly into 24 we can create an equivalent fraction from 3/4 to 18/24 (multiply numerator and denominator by 6)

now you can add:

[tex]\frac{15}{24}[/tex] + [tex]\frac{18}{24}[/tex] = [tex]\frac{(15+18)}{24}[/tex] = [tex]\frac{33}{24}[/tex]

since the numerator is larger than the denominator this is called an improper fraction and can be changed into a mixed number by dividing 24 into 33

24 goes into 33 one time with a remainder of 9

so 33/24 = 1 [tex]\frac{9}{24}[/tex] wherein 9 and 24 can each have a 3 factored out to make it fully simplified

9÷3 = 3

24÷3 = 8

final answer is 1 [tex]\frac{3}{8}[/tex]

Answer:

11/8 is the correct answer

Step-by-step explanation:

15/24 + 3/4

Reduce the fraction   15/24 ​   to lowest terms by extracting and canceling out 3.

=5/8 +3/4

Least common multiple of 8 and 4 is 8. Convert 5/8 and 3/4 to fractions with denominator 8.

= 5/8 + 6/8

since 5/8 and 6/8 have the same denominator, add them by adding their numerators.

= 5 + 6/8

Add 5 and 6 to get 11.

=11/8

here is why 9/14 is wrong

on tuesday a local a hamburger shop sold a combined total of 448 hamburgers and cheeseburgers , the number of cheeseburgers sold was three times the number of hamburgers sold how many hamburgers were sold on tuesday ?

Answers

Cheeseburger=3/4
Hamburgers=1/4
448/4=112
112x3=336
Cheeseburgers=336
Hamburgers=112
112 hamburgers were sold on Tuesday.

One hundred voters were asked whether they supported a bill that had

Answers

The question is cut off.

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

Answers

The answer is in the picture below .
1/y3 hope this helps

A store manager kept track of the number of newspapers sold each week over a seven-week period. The results are shown below.
81 71 202 113 269 248 242
Find the median number of newspapers sold.
CE
O A. 242 newspapers
OB 175 newspapers
OC. 113 newspapers
OD. 202 newspapers

Answers

OD Step-by-step explanation:

The median of the of the number of newspapers sold by shopkeeper is 202 .

Given,

A store manager kept track of the number of newspapers sold each week over a seven-week period.

81 71 202 113 269 248 242.

Now,

The median of the dataset is the middle value of the dataset, which means that 50 % of the values are below the mean and 50% of the values are above the mean.

Rearrange the dataset in ascending order as

71, 81, 113, 202, 242, 248, 269.

Thus the median will be the 4th value.

Hence the median will be 202.

Thus the correct option will be 202 Newspapers.

Know more about median,

https://brainly.com/question/300591

#SPJ4

How can you solve multistep equations that represent real world
scenarios?

Answers

Yeah like you can do scenarios or examples or you can get creative

Given ω=[tex]\frac{3-2i}{5-6i}[/tex] , find ω in the a+bi form.

Answers

Answer:

Solution is given in the photo

I need help solving this problem

Answers

What is the problem you are trying to solve

what is the value of x that makes the equation 8 x -4 equal 96 true​

Answers

Answer:

x= 12.5 or 25/2

Step-by-step explanation:

8x - 4 (+4) = 96 (+4)

8x (/8) = 100 (/8)

x= 12.5 or 25/2

Hi guys can u guys help me add 322 + 12

Answers

Answer:

334 is the answer

Step-by-step explanation:

you add them together

Answer:

334 is the right answer

Step-by-step explanation:

please mark me brainliest

Solve this plz question plz​

Answers

We have: [tex](-\frac{15}{18})[/tex] ÷ [tex](-\frac{20}{24})[/tex] = [tex]\frac{-15}{18} .\frac{-24}{20} = \frac{(-3)(5).(-4)(6)}{(3)(6).(4)(5)} = 1[/tex]

ANSWER: 1

ok done. Thank to me :>

Answer:

1

Step-by-step explanation:

[tex]( - \frac{15}{18} ) \div ( - \frac{20}{24} ) \\ now \: you \: have \: fraction \: divided \: by \: fraction \: then \: do \: reciprocal \: \\ ( - \frac{15}{18} ) \times ( - \frac{24}{20} ) \\ = 1[/tex]

Solve the equation square root of x-2+5 = 7 for the variable. Show each step of your solution process

Answers

Answer:

x=4

Step-by-step explanation:

x+3=7

subtract 3 from both sides

simplify

order the expression from least to greatest

Answers

Answer:

So it would be 4, 11, 20

Step-by-step explanation:

[tex]11^1 = 11[/tex]

[tex]2^2 * 5 = 20[/tex]

[tex]8^2-60 =4[/tex]

Which equation represents this line in point-slope form?

A.
`(y + 4) = (4)/(3) (x + 3)`

B.
`(y −4) = -(4)/(3) (x +3)`

C.
`y= -(3)/(4)x`

D.
`4y− 3x = 0`

Answers

Answer:

The Answer is Option A or Option B

Step-by-step explanation:

First let's review what point slope form is.

[tex]y - y 1 = m(x - x1)[/tex]

To take a line and put it into point slope form you need to identify one of the points. In this case the point is either (-3, -4) or (-3, 4) but without a graph attached I cannot personally say which one it is.

You will also need to identify the slope of the line (m) based on the graph, so identify if the graph is ascending or descending. This alone can determine your answer

Again, there is no graph provided so it is up to you to determine if it is Option A or B.

I really hope this helps and you have a great rest of your day!

Note: I am not a professional educator so take my opinion carefully.

=)

George is building a rabbit run in his backyard he makes the length 2/7km and the width 1/5km draw a sketch of his rabbit run and then find the area

Answers

Here !

I hope this helps you a little ,

What is the length of LN in the right triangle below?

Answers

Answer:

D 280

Step-by-step explanation:

Pythagoras theorem

Answer:

a

Step-by-step explanation:

LN=√19^2 - 9^2

=√361 - 81

=√280

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