verify the identity

[tex]cot(x-\frac{\pi }{2} )[/tex] = - tan x

please show all steps

Answers

Answer 1

Answer:

Step-by-step explanation:

[tex]\tan (x-\frac{\pi }{2} )=\frac{tan~x-tan~\frac{\pi }{2} }{1+tan~x~tan~\frac{\pi }{2} } \\or~\cot(x-\frac{\pi }{2} )=\frac{1+\tan~x~\tan\frac{\pi }{2} }{\tan~x-\tan~\frac{\pi }{2} } \\divide~the~R.H.S. ~by~\tan ~x~\tan~\frac{\pi }{2} \\=\frac{\cot~x~\cot~\frac{\pi }{2} +1 }{\cot~\frac{\pi }{2} -\cot~x} \\\cot\frac{\pi }{2} =0\\\cot(x-\frac{\pi }{2} )=\frac{\cot~x ~\times~0+1}{0-\cot~x} \\\cot~(x-\frac{\pi }{2} )=-\frac{1}{\cot~x} =-\tan~x[/tex]


Related Questions

is social media company conducted research on the number of our high school students are on social media and the hours of leaf they receive based on the scatterplot in the image what is the best prediction of the number of hours a high school school student sleeps when he spends 1 hour and social media​

Answers

Answer:

8.5 hours

Step-by-step explanation:

Draw a line of best fit to predict

Write an equation for the following table.

Answers

Answer:

y= 38x

Step-by-step explanation:

It is going up by 38 each time. There is no b value (y=mx + b), because if you times 6 by 38, you get 228. You don't need to add any remainders.

Circle the fraction equal to 0.1%

Answers

0.1 as a fraction in simplest form is 1/10. For this answer, you simply have to replace the point with 10 in the denominator.

HELO URGENT WILL GIVE BRAINLIEST IF CORRECT

Answers

Answer:
Circle

Explanation:
The answer is circle
Hope this helps

Plsss help ASAP the semester is about to end and I have to finish so many assignments

Answers

Answer:

f(15,055) is the number of pages in a book with 15,055 words.

Step-by-step explanation:

f(w) = length of book (in pages).

w = number of words

Thus, from the options given, the only true statement about the function is that:

f(15,055) = number of pages of a book that has 15,055 words.

"f(15,055)" is the length of a book consisting of 15,055 words. It does not imply that there are 15,055 pages.

Juan bought fruit from the grocery store. The variables below define his purchase. Juan’s bananas cost half as much as apples. Which equations can be used to model his purchase? Select each correct equation. *

Answers

Answer:

[tex]B = \frac{1}{2}A[/tex]

[tex]A = 2B[/tex]

Step-by-step explanation:

Given

Represent apple with A and Banana with B

Required

Determine the relationship between A and B

From the question, we understand that:

B costs half as much as A

This can be represented as:

[tex]B = \frac{1}{2} * A[/tex]

[tex]B = \frac{1}{2}A[/tex]

Multiply both sides by 2

[tex]2*B = \frac{1}{2}A*2[/tex]

[tex]2B = A[/tex]

[tex]A = 2B[/tex]

Sry the app makes the photo so bad quality but anyways can someone please help me

Answers

The answer is option d because both angle one and angle three are vertically opposite angles

6x+45=9x+15

Collect like terms

-3x=-30

Divide both sides by -3

-30/-3 is 10

So, the answer is d

Answer:

B also the full name of vertically angles is called the vertically opposite angle theorem or voat

A. 3(x+2)=18 B. 3x+6=18

Answers

Answer:

B

Step-by-step explanation:

3x6 is 18 so therefore its B

what the quest but I guess A or B but I

The perimeter of a polygon is 96 ft.
Write and solve an equation to find “m”.

Answers

Answer:

m = 12

Step-by-step explanation:

Total perimeter = 3m + 3m + m + m = 96

so, 8m = 96

then m = 12

Can someone help me I have two more other questions they are 15 points each I just posted them right now! Thanks so much I will give brainliest

Answers

The measure of each of the vertical angles is 85 degrees.

It’s established that both of these angles are equal to each because they’re vertical equals. With this information we can make the equation 2x + 65 = 8x + 5. We then solve this equation for x.

2x + 65 = 8x + 5

60 = 6x

x = 10

We then plug the value of x into either of the equations for the angles, giving us the answer 85.

Answer:

80˚

Step-by-step explanation:

Since the angles are equal, we can make this equation:

2x + 65 = 8x + 5

60 = 6x

x = 10

so if we put x = 10 in 8x + 5 we get

8x + 5

8(10) + 5

80 + 5

85

help help help help help​

Answers

Answer:

Step-by-step explanation:

1) (-6 , 2) ; (3 , -5)

Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

         [tex]= \frac{-5-2}{3-[-6]}\\\\= \frac{-5-2}{3+6}\\\\= \frac{-7}{9}\\[/tex]

m = -7/9 ; (-6 , 2)

y - y₁ = m(x -x₁)

y - 2 = (-7/9)(x - [-6])

[tex]y - 2 = \frac{-7}{9}(x + 6)\\\\y -2 = \frac{-7}{9}x + \frac{-7}{9}*6\\\\y - 2 = \frac{-7}{9}x - \frac{7*2}{3}\\\\ y = \frac{-7}{9}x - \frac{14}{3} + 2\\\\y = \frac{-7}{9}x -\frac{14}{3} + \frac{2*3}{1*3}\\\\y = \frac{-7}{9}x - \frac{14}{3} + \frac{6}{3}\\\\y = \frac{-7}{9}x - \frac{8}{3}[/tex]

2) (3 , -4) ; m= 3

[tex]y - y_{1} = m(x - x_{1}[/tex])

y - [-4] = 3(x - 3)

y + 4 = 3x - 3*3

y + 4 = 3x  - 9

     y = 3x - 9 - 4

Ans: y = 3x - 13

3) m = 2 ; y-intercept (b) = 3/2

     y = mx + b

  Ans: y = 2x + (3/2)

4) (-1, 3 ) ;  (2 , 0)

Slope = [tex]\frac{0 - 3}{2-[-1]}[/tex]

         [tex]= \frac{-3}{2+1}\\\\= \frac{-3}{3}\\\\= 1[/tex]

m = 1; ( -1 , 3)

y - 3 = 1(x -[-1])

y - 3 = 1(x + 1)

y - 3 = x + 1

    y = x + 1 + 3

  Ans: y = x + 4

5)(2, 1) ;m = -3

y - 1 = (-3)(x - 2)

y - 1 = -3x + 6

   y = -3x + 6 +1

Ans: y = -3x + 7

Step-by-step explanation:

1) (-6 , 2) ; (3 , -5)

Slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}

x

2

−x

1

y

2

−y

1

\begin{gathered}= \frac{-5-2}{3-[-6]}\\\\= \frac{-5-2}{3+6}\\\\= \frac{-7}{9}\\\end{gathered}

=

3−[−6]

−5−2

=

3+6

−5−2

=

9

−7

m = -7/9 ; (-6 , 2)

y - y₁ = m(x -x₁)

y - 2 = (-7/9)(x - [-6])

ABCDE~GHJDF Complete statement

Answers

Answer:

FE

Step-by-step explanation:

i hope you help this answer

For the two similar figures, the expression can be written as:

[tex]\dfrac{GH}{AB} = \dfrac{JD}{CD}[/tex]

What is the similarity?

In geometry, similarity refers to the property of two figures that have the same shape but possibly different sizes. Two figures are considered similar if their corresponding angles are congruent and their corresponding sides are proportional.

For example, two triangles are similar if they have the same shape but can be different in size. This means that the corresponding angles of the two triangles are equal and the corresponding sides are in proportion.

The symbol used to denote similarity is "~". For example, if triangle ABC is similar to triangle DEF, we write it as:

ABCDE~GHJDF are similar. So the ratios of the sides of the figure can be written as,

[tex]\dfrac{GH}{AB} = \dfrac{JD}{CD}[/tex]

To know more about similarity follow

https://brainly.com/question/30068992

#SPJ7

please answer the question below

Answers

Answer: 220

Step-by-step explanation:

Will already has 148 he bought 8 packages that contains 9 in each so 8 x 9 = 72 then add 148 to 72 and you will have your total which is 220.

2. The ratio of boys to girls in Spanish class is 2:4. If there are 24 total students in class, how many boys and
girls are there?
Boys
Girls

Answers

Answer:

there are 8 boys and 16 girls

hope this helped :-)

Step-by-step explanation:

24:4=6

6+2=8

8+8=16

8:2=4

8+8+4+4=24

4+4=8

The temperature outside changed from 66°F to 42°F over a period of eight days. If the temperature changed by the same amount each day, what was the daily temperature change?

Answers

Now I don’t know if this is right but I’m pretty sure it’s just 24 with simple subtraction

Which is a better state?
Ny or Florida
(Doing this for a statistic question)

Answers

Answer:

I would personally say Florida. When looking at things such as race, NYC has many races, and New York has very different neighborhoods and lifestyles.

In Florida, most people are more laid back, and there are not that many differences in race and other aspects.

The movie starts at 3:15 p.m. and ends at 5:08 p.m. How long is the movie?

Answers

Answer:

1 hour and 53 minutes

Step-by-step explanation:

Your welcome


Since starting a new recycling plan, Aaron's office recycles 7 kilograms of paper each week,
How many weeks will it take Aaron's office to recycle a total of 28 kilograms of paper?

Answers

Answer: 4 weeks

Step-by-step explanation: 28 divided by 7 is 4.

Find x & y so that quadrilateral is a parallelogram. (Look at image)

Answers

Answer:

x = - 6 y = 13

Step-by-step explanation:

we know when the diagonals bisect it divides into two equal parts so

-4x - 2 = -3x + 4

-4x + 3x = 4 + 2

- x = 6

x = - 6

Now

2y + 8 = 3y - 5

3y - 2y = 8 + 5

y = 13

Hope it will help :)❤

please help :) worth 10 points

Answers

what the other personnsaid is correct

Answer:

a. (0,3)

b. (-4,-3)

c. (-2,0)

d. (-1 1/3, 1)

e. (4,9)

f. (-3 1/3, -2)

Step-by-step explanation:

(x-2)(x+8)=0 Solve for x

Answers

X - 2 = 0
X + 8 = 0

X= 2
X= -8
x - 2 = 0
x + 8 = 0

1. Add 2 to both sides to isolate x.
2. Subtract 8 to both sides to isolate x.

x = 2
x = -8

in the problem find m<1​

Answers

Answer:

m∠1 = 124°

Step-by-step explanation:

If this is the case then m∠1 and m∠2 are congruent to each other with the same angle in which m∠2 is also 124°, if m∠3 is said to be 56°.  Also, a straight angle has to equal to 180° in which the first angle is classified as obtuse.

Can the sides of a triangle have lengths 1, 5, and 5?
Yes or no?

Answers

Answer:

Yes it can have the lengths 1, 5 and 5

1) Diego drank x ounces of juice. Lin drank 1/4 less than that

2) Lin ran x miles. Diego ran 3/4 more than that

3) Diego bought x pounds of almonds Lin bought 1/4 of that


(Drag and drop plz help)

Answers

Answer:

Follows are the solution to this question.

Step-by-step explanation:

Please find the solution file for the question in the attachment.

91 points need help now . Emanuel put 12 marbles on one pan
of a scale. On the other pan, he put
4 marbles, then he added 8 more
marbles to that side. Each of the-
marbles weighs 1 ound. Is the scale
balanced? Explain.

Answers

Answer: I believe the scale is balanced.

Step-by-step explanation: I stated that because since the other side of the scale contained 12 marbles that were 1 pound each that would be 12 pounds and then since 4+8=12 12 pounds of marbles were also put on the other side.

B
113°
72°
А
с
D
Write a list of steps that are needed to find the measure of ZB.

Answers

Step-by-step explanation:

the exterior angle is equal to the sum of the interior angles on the opposite side.

As in angle BCD = angle BAC + angle ABC

113 = 72+angle ABC

angle ABC = 41

Answer:

180-113 to find the linear angle.

add that result with 72.

once found the sum, use 180 to subtract the sum to get angle B.

write an expression that is equivalent to 1/3x+3/4+2/3x-1/4-1/3-2/3x

Answers

Answer: 1/3x + 1/6

Step-by-step explanation:

The expression that is equivalent to 1/3x+3/4+2/3x-1/4-1/3-2/3x would be:

= 1/3x + 2/3x - 2/3x + 3/4 - 1/4 - 1/3

= 1/3x + 3/4 - 1/4 - 1/3

= 1/3x + 1/2 - 1/3

= 1/3x + 3/6 - 2/6

= 1/3x + 1/6

Answer:

1/3x + 2/4

Step-by-step explanation:

(1/3x + 2/3x = 3/3x/ 1 - 2/3 = 1/3) (3/4 - 1/4 = 2/4

Kevin wants to buy a new pair of jeans if the jeans were originally $40 but are on sale with 25% discount
how much will Kevin have to pay for the jeans?

Answers

Answer: Kevin will have to pay $30 for the jeans.

Answer:

He will have to pay 30$

Step-by-step explanation:

What is the expression of 82 and 95

Answers

Answer: 88.5

Step-by-step explanation:

Step 1: Address the formula, input parameters & values.

Input parameters & values:

The given numbers are 82 & 95

Step 2: Find the sum of the given two numbers.

sum = 82 + 95 = 177

Step 3: Divide the sum by 2 to get the average.

average = 177/2

= 88.5

Evaluate −4(14)6x for x=13. Enter your answer as a fraction in simplest form in the box.

Answers

-15228 I think but let me know if I’m wrong please
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