Please simplify the following trigonometric identity.

[tex]\displaystyle\frac{1}{\sec\alpha-\tan\alpha}[/tex]

Answers

Answer 1

Examining the question:

We are given the expression:

[tex]\frac{1}{Sec(\alpha)-Tan(\alpha)}[/tex]

We know from Basic trigonometry that:

[tex]Sec(\alpha) = \frac{1}{Cos(\alpha)}[/tex]

[tex]Tan(\alpha) = \frac{Sin(\alpha)}{Cos(\alpha)}[/tex]

Simplifying the expression:

Replacing these values in the given expression, we get:

[tex]\frac{1}{\frac{1}{Cos(\alpha)} -\frac{Sin(\alpha)}{Cos(\alpha)} }[/tex]

Since the denominator of both the values in the denominator is the same:

[tex]\frac{1}{\frac{1-Sin(\alpha)}{Cos(\alpha)} }[/tex]

We know that [tex]\frac{1}{\frac{a}{b} }[/tex] = [tex]\frac{b}{a}[/tex], using the same property:

[tex]\frac{Cos(\alpha)}{1-Sin(\alpha)}[/tex]

and we are done!

Answer 2

Answer:

cos a

---------------------

1  -sin (a)

Step-by-step explanation:

We know that sec a = 1/ cos (a)  and tan a = sin (a) / cos (a)

1

---------------------

1/ cos (a)  -sin (a) / cos (a)

Multiply the top and bottom by cos (a)

1* cos a

---------------------

( 1/ cos (a)  -sin (a) / cos (a)) * cos a

cos a

---------------------

1  -sin (a)


Related Questions

Which fraction is marked by the point on the number line?

Answers

Answer:

where is the numer line?

Step-by-step explanation:

Help! Will give brainliest to first correct answer.

Answers

Answer:

a) 7n

b) n+7

c) n -7

d). [tex]\frac{n}{7}[/tex]

Step-by-step explanation:

All you have to do for this question is look at the key words. These will help you find the correct answers.

Product = multiplication (x)Sum = addition (+)Difference = subtraction (-)Quotient = Division

Find the length of the third side. If necessary,
round
to
the nearest tenth.
4
7

Answers

Answer:

The answer would be 8.1

Step-by-step explanation:

At art class, Mr. Gibson spends 5 minutes giving instructions, 35 minutes working on the project, and 15 minutes cleaning up. If class starts at 1:15 PM, what time will it end? PM​

Answers

Answer:

2:10 PM

Step-by-step explanation:

5+35+15=55 mins

1:15+55 mins=2:10PM

the answer you need is 2:10 pm. hope that helps

A bucket has 16 tennis balls and 10 ping pong balls . What is the probability of selecting a ping pong ball , replacing it and then selecting a tennis ball

Answers

Answer:

40/169

Step-by-step explanation:

P(pp,tennis) = [tex]\frac{10}{26}[/tex] × [tex]\frac{16}{26}[/tex] = 40/169 in simplified form

The probability of selecting a ping pong ball, replacing it and then selecting a tennis ball is 40/169.

What is Probability?

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

We have,

Tennis ball = 16

Ping pong balls = 10

So, probability of selecting a ping pong ball, replacing it and then selecting a tennis ball

= 10/ 26 x 16/26

= 40/169

Learn more about Probability here:

https://brainly.com/question/11234923

#SPJ7



Which
Charles factors the expression 9 x + gx using a factor of 5 x. He writes the factored expression as 3 «(4x+1).
best describes the accuracy of Charles's solution?
His solution is accurate,
His solution is inaccurate. The factor does not divide evenly into both terms.
O His solution is inaccurate. The factoring of g xy using the given GCF is incorrect.
His solution is inaccurate. The factoring of 3 using the given GCF is incorrect.

Answers

Step-by-step explanation:

Charles factors the expression Four-thirds x y + one-third x using a factor of One-third x. He writes the factored expression as One-third x (4 y + 1). Which best describes the accuracy of Charles’s solution?

His solution is accurate.

His solution is inaccurate. The factor does not divide evenly into both terms.

His solution is inaccurate. The factoring of Four-thirds x y using the given GCF is incorrect.

His solution is inaccurate. The factoring of One-third x using the given GCF is incorrect.

i hope you understand

Which of the following is the correct way to state the similarity between these two figures?

A.) ABCDE ~ YXVZW


B.) ABCDE ~ VWXYZ


C.) ABCDE ~ VZWYX


D.) ABCDE ~ ZWYXV

Answers

Answer:

ABCDE is similar to the ZWYXV

Please help I don’t gat this

Answers

Answer:

30 yards

Step-by-step explanation:

the dotted line causes a rectangle and a triangle to be formed. the formula for area of a triangle is base times height divided by 2. you subtract 6 from 9 which is 3 and multiply it by 4 as it is the height of the triangle after, divide by 2 . since 4 and 3 is 12, dividing 12 by 2 is 6 which is the area of the triangle. the area of the rectangle is 6 times 4 which is 24. add 24 and 6 and u get 30

IS THIS IN SIMPLIST FORM? PLEASE HELP! TY!

2( x - 3 + 2 )

Answers

Answer:

2x - 2

Step-by-step explanation:

There are two steps to take here.  First add together the -3 + 2 in the brackets:

2(x - 3 + 2)

= 2(x - 1)

Now use the distributive property and multiply each term in the brackets by two:

2(x - 1)

= 2x - 2

And you now have it in simplest form.

A heavy rope, 50 ft long, weighs 0.6 lb/ft and hangs over the edge of a building 120 ft high. Approximate the required work by a Riemann sum, then express the work as an integral and evaluate it.

Exercise (a)

How much work W is done in pulling the rope to the top of the building?

Exercise (b)

How much work W is done in pulling half the rope to the top of the building?

Answers

Answer:

Exercise (a)

The work done in pulling the rope to the top of the building is 750 lb·ft

Exercise (b)

The work done in pulling half the rope to the top of the building is 562.5 lb·ft

Step-by-step explanation:

Exercise (a)

The given parameters of the rope are;

The length of the rope = 50 ft.

The weight of the rope = 0.6 lb/ft.

The height of the building = 120 ft.

We have;

The work done in pulling a piece of the upper portion, ΔW₁ is given as follows;

ΔW₁ = 0.6Δx·x

The work done for the second half, ΔW₂, is given as follows;

ΔW₂ = 0.6Δx·x + 25×0.6 × 25 =  0.6Δx·x + 375

The total work done, W = W₁ + W₂ = 0.6Δx·x + 0.6Δx·x + 375

∴ We have;

W = [tex]2 \times \int\limits^{25}_0 {0.6 \cdot x} \, dx + 375= 2 \times \left[0.6 \cdot \dfrac{x^2}{2} \right]^{25}_0 + 375 = 750[/tex]

The work done in pulling the rope to the top of the building, W = 750 lb·ft

Exercise (b)

The work done in pulling half the rope is given by W₂ as follows;

[tex]W_2 = \int\limits^{25}_0 {0.6 \cdot x} \, dx + 375= \left[0.6 \cdot \dfrac{x^2}{2} \right]^{25}_0 + 375 = 562.5[/tex]

The work done in pulling half the rope, W₂ = 562.5 lb·ft

A brochure claims that the average maximum height a certain type of plant is 0.7 m. A gardener suspects that this estimate is not accurate locally due to soil conditions. A random sample of 43 plants is taken. The mean height of the plants in the sample is 0.65m. Using a 1% level of significance, perform a hypothesis test to determine whether the population mean is different from 0.7m. Assume that the population standard deviation is 0.2 m.

Answers

Answer:

We accept the null hypothesis, that is, that the population mean is not different from 0.7.

Step-by-step explanation:

A brochure claims that the average maximum height a certain type of plant is 0.7 m.

This means that the null hypothesis is:

[tex]H_{0}: \mu = 0.7[/tex]

A gardener suspects that this estimate is not accurate locally due to soil conditions.

Hypothesis test to determine whether the population mean is different from 0.7m, which means that the alternate hypothesis is:

[tex]H_{a}: \mu \neq 0.7[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.7 is tested at the null hypothesis:

This means that [tex]\mu = 0.7[/tex]

A random sample of 43 plants is taken. The mean height of the plants in the sample is 0.65m.

This means, respectively, that [tex]n = 43, X = 0.65[/tex]

Assume that the population standard deviation is 0.2 m.

This means that [tex]\sigma = 0.2[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.65 - 0.7}{\frac{0.2}{\sqrt{43}}}[/tex]

[tex]z = -1.64[/tex]

Pvalue of the test:

Since we are testing that the mean is different of a value, and z is negative, the pvalue of the test is 2 multiplied by the pvalue of z = -1.64

z = -1.64 has a pvalue of 0.0505

2*0.0505 = 0.101

Using a 1% level of significance, perform a hypothesis test to determine whether the population mean is different from 0.7m.

0.101 > 0.01, which means that we accept the null hypothesis, that is, that the population mean is not different from 0.7.

Is 60.560 an irrational number or rational?

Answers

Answer: ratinal?

Step-by-step explanation:

Margo can purchase tile at a store for $0.59 per tile and rent a tile saw for $49. At another store she can borrow the tile saw for free if she buys tiles there for $1.29 per tile. How many tiles must she buy for the cost to be the same at both stores?


Margo must buy
tiles for the cost to be the same at both stores.

Answers

Answer:

Also need help

Which statement best describes the function?
O A. The function is increasing when x < 0.
B. The function is decreasing when x > 0.
C. The function is never increasing.
D. The function is always increasing.

Answers

Answer:

D. The function is always ingcreasing

please help!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

I am not sure but think that the answer is 1/20

I believe you convert the whole number into a mixed fraction.

5 converted into quarters is 20/4. Then you divided 1/4 by 20/4.

1/4 divided by 20/4 is 1/20 or 0.05.

Please, don't refrain to tell me if this is incorrect. Thank you.

Assume v is a vector in R^5. You wish to compute a vector w such that the th entry of w, denoted wi, is the sum of vi-1,vi, vi+1. For example wi is the sum of ,vo,v1 and v2. For elements at the endpoints of w, you will only account for two elements in your sum. For example wo, (assuming zero-based indexing) is the sum of vo and v1. Construct a matrix A such that Av=w.

Answers

Answer:

Use the drawing tools to form the correct answer on the graph.

Graph the line that represents this equation:

Step-by-step explanation:

Solve similar triangles
Solve for x
X=?

Answers

Answer:

x = 5

Step-by-step explanation:

AB/BC = AD/DE

9/3 = 15/x

9x = 45

x = 5

may kapangyarihan bilang pinakamataas na hukuman sa kolonya​

Answers

Answer:

which language is this .

Write an emergency that could happen that would have a financial cost

Answers

Answer:

Your house burning down.

Step-by-step explanation:

You would have to pay to repair it.

Answer:

Earthquake will make the building crash and people will lost their things and money. And the building need to rebuild.

The building fire will make people lost their things and the building need to rebuild.

Tsunami will make the things near beach all destroy, all the things will lost and more people will die in disaster. All the building need to rebuild in this disaster.

Bank robbery will lost money, sometimes people will kill by the gun of the thief, and the building do not need to rebuild, maybe the window need to rebuild.

Rob the shop will make the boss of the shop lose all the money in the store, the door or window might need to rebuild.

Blasting vehicle will make the things in the car lose. the car need to put the windows on again.

Terrorist attacks will lost lives more than lost money or other things.

Volcanic eruptions will make the building near burn, and so plant and many other things. The building might need to rebuild.

That is all I can think of.

um what do i do here

Answers

Answer:

you add and subtract

Step-by-step explanation:

You need to match the sum/difference with the expression

Example -

A. 5x+2x 15x+2y (B)

B. 7x+8x+2y. 7x (A)

That's how you match it

The hanger image below represents a balanced equation. Find the value of n that makes the equation true.

Answers

Answer:

6

Step-by-step explanation:

16=n +10

subtract 10 from both sides and your left with 6=n

The answer is 6, I already this and it’s pretty easy

Calculate the volume of this triangular prism?

Answers

Answer:

960 sq cm

Step-by-step explanation:

(16*12*10)/2

Can Someone please help me !!! ( you have to fill out the blanks )

Answers

Answer:

1. 5(a-6) = 5a-30

2. 2(3a-b) = 6a-2b

3. 5(-5x+3) = -25x+15

4. -(2c+3) = -2c-3

Both of their first step are correct (Show your calculations to explain)

x-9 = 5

x = 14

2x-18 = 10

2x = 28

x = 14

Step-by-step explanation:

All Above

find the slope


!!!!!please help QUICK!!!!

Answers

Answer:

3/4

Step-by-step explanation:

We can find the slope using two points

( 0,-5) and ( 4,-2)

The slope is given by

m = ( y2-y1)/(x2-x1)

   = ( -2- -5)/( 4-0)

    = (-2+5)/(4-0)

     =3/4

PLEAS HELP THERE IS PIC drag the tiles to the correct boxes to complete the pairs. how many solutions does each equations have ?

Answers

Answer:

|2x+1|=0 has one solutions

2|x+1|=-2 has no solution

|x+21|=2 has two solution

Step-by-step explanation:

Anyone can help with this

Answers

Answer:

C

Step-by-step explanation:

Notice how C is the only function that is quadratic. If you expand (2x-1)^2, you get 4x^2-4x+1. Since x is raised to the power of two, it isn't linear, but quadratic.

Answer:

C

Step-by-step explanation:

i used photomath and C was not the linear one!

Please help me with this :)

Answers

[tex]hope \: it \: helps[/tex]

Function Notation
If f(x) = -3x2 + 2x - 8, find each of the following:

f(-1)
f(0)
f(3)
f(1/3)

Answers

I checked all answers on Photomath.
Let me know if that’s helpful.

A bag of 4 balls weighs 6 pounds. Each ball weighs the same amount. What is the weight of each ball?

Answers

6/4 = 1.5
Answer: 1.5 pounds

abc~def what sequence of transformation will move ABC onto def ​

Answers

Answer:

c

Step-by-step explanation:

Answer:

is C guys

Step-by-step explanation:

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