Show that sec(x)-tan(x)sin(x)=cos(x)is an identity for any value of x.

Answers

Answer 1

Here is one way to show that the left side is identical to the right side.

[tex]\sec(x)-\tan(x)\sin(x) = \cos(x)\\\\\\\frac{1}{\cos(x)}-\frac{\sin(x)}{\cos(x)}\sin(x) = \cos(x)\\\\\\\frac{1}{\cos(x)}-\frac{\sin^2(x)}{\cos(x)} = \cos(x)\\\\\\\frac{1-\sin^2(x)}{\cos(x)} = \cos(x)\\\\\\\frac{\cos^2(x)}{\cos(x)} = \cos(x)\\\\\\\cos(x)=\cos(x)\\\\\\[/tex]

Throughout the entire process, the right hand side stayed the same. When working on identities, it's important to keep one side the same while you transform the other side.

Despite the two sides being identical when simplified, there is the issue of cos(x) being zero in the denominator on the left hand side. Be sure to account for this when forming the domain. No such issue occurs on the right hand side. For instance, the value x = pi/2 leads to a division by zero error when in radian mode. So if I was your teacher, I would revise the "for any value of x" and replace it with something along the lines of "for any x value in the domain".


Related Questions

Which of the following functions are solutions of the differential equation y" + y = 7 sin(x)? (Select all that apply.)

y = 7 sin(x)
y= 7 cos(x)
y= 7x sin(x) - 8x cos(x)
y = 7/2 sin(x)
Y = - 7/2 cos(x)

Answers

The homogeneous equation

y'' + y = 0

has characteristic equation

r² + 1 = 0

with roots at r = ± √(-1) = ± i, and so the characteristic solution is

y = C₁ cos(x) + C₂ sin(x)

Using the method of undetermined coefficients, suppose

y = a x cos(x) + b x sin(x)

(we would normally consider y = a cos(x) + b sin(x), but cos(x) and sin(x) are already part of the characteristic solution)

The derivatives are

y' = a cos(x) - a x sin(x) + b sin(x) + b x cos(x)

y' = (b - a x) sin(x) + (a + b x) cos(x)

and

y'' = -a sin(x) + (b - a x) cos(x) + b cos(x) - (a + b x) sin(x)

y'' = (-2a - b x) sin(x) + (2b - a x) cos(x)

Then

y'' + y = (-2a - b x) sin(x) + (2b - a x) cos(x) + a x cos(x) + b x sin(x)

7 sin(x) = -2a sin(x) + 2b cos(x)

and it follows that a = -7/2 and b = 0.

So, the general solution to the DE is

y = C₁ cos(x) + C₂ sin(x) - 7/2 x cos(x)

which means the only valid solutions from the given choices are

y = 7 sin(x)

y = 7 cos(x)

I have a Statistics question​

Answers

Answer:

okayyyyyyyyyyyyyyyy

Step-by-step explanation:

have a nice day

okkkkkkkkkkkkkkkkkkkkkkkk

A mechanic is paid $61,490 in salary for a year. Assuming there are 26 pays in a year, what is her biweekly (average) salary? $30,745 $3,074.50 $1,182.50 $2,365​

Answers

Answer:

$2,365

Step-by-step explanation:

Divide $61,490 by 26...

Do both of them for 50 points

Answers

Answer:

1) 7/12, 2) 7/24

Step-by-step explanation:

Just plug in the values of c and d.

1) given: c = -1 1/4, d = -1

1/3 * (-1 1/4) - (-1)^3 = -5/12 + 12/12 = 7/12

(-1^3 is -1 (there's a positive in front as well so the negatives cancel out and it's just 1) and then convert everything to a common denominator (which is 12). 1/3 times -1 1/4 becomes -5/12 when you multiple straight across).

2) given: c = 4 1/4, d = 1 1/2

1/3 * (4 1/4 - (1 1/2)^3) = 1/3 * (17/4 - 27/8) = 1/3 * (34/8 - 27/8) = 1/3 * 7/8 = 7/24

(use pemdas/order of operations and solve the exponent first, then the parentheses. 1 1/2^3 is 27/8, and 4 1/4 is 34/8. when you subtract you get 7/8, then you can multiply straight across with 1/3 and you get 7/24.)

Compound interest compounded quarterly is given every ______ months. *
1 point
1
3
6
Compound interest compounded semiannually is given every ___ months. *
1 point
1
3
6
The algebraic equation for interest is______. *
1 point
y=mx+b
e=mc2
i=prt
Principal $2000, rate 3.1%, 2 months, compounded monthly. Calculate the balance at the end of 2 months. *
1 point
$2010.35
$2025.62
$2003.10
What is your favorite Christmas cookie? *
1 point
chocolate chip
sugar cookie
peanut butter
other
Calculate the simple interest earned: principal $1000, rate 4%, 7 days *
1 point
$10.00
$0.77
$23.33

How is compound interest similar to a snowball rolling down a snow covered hill? *
1 point
The interest rate used to calculate earned interest is represented as a percent. True or False *
1 point
True
False
First name *
Given the same principal, rate and time which investment calculation would earn less? *
1 point
simple interest
compound interest
Last name *
Which word refers to the money deposited into an interesting bearing account ? *
1 point
cash
principal
bling

Answers

Answer:

3 months, 6 months, interest is 1 point or 0.01 for every percent, 2010.35, peanut butter but why is this a question, 0.77, It is similar to a snowball because as time goes on the account grows at the same percent but it is more money so it is a larger amount. This is very common in dividend investing. next question, yes it is a percent, simple because compound is always more or the same, I would say principal but I am not sure

Step-by-step explanation:

America says that the point (0,0) on the graph below means that you use no sugar if you make 1 pie. Is America correct? ​

Answers

Answer:

America is correct

Step-by-step explanation:

it says 0,0 and then it would mean it wouldn't have any sugar in the pies

Answer:

No, America's wrong.

If you look on the graph, as the line increases you can see one pie needs around 3/4(not accurate). (0,0) is the origin point. No sugar is used, and no pie was made.

On a human, what is the ratio of arms to fingers?

Answers

Total arms in human body=2Total fingers in human body =5+5+5+5=20(10 of hands and 10 of legs)

Ratio:-

[tex]\\ \sf\longmapsto \dfrac{2}{20}[/tex]

[tex]\\ \sf\longmapsto \dfrac{1}{10}[/tex]

[tex]\\ \sf\longmapsto 1:10[/tex]

1. According to the fundamental theorem of algebra, how many zeros does the function [tex]f(x) = 3x^6 - 7x^5 - 53x^3 - 43x - 34[/tex] have?

2. What are the zeros of [tex]f(x) = 6x^3 + 25x^2 - 24x + 5[/tex]

Answers

Answer:

See below for answers

Step-by-step explanation:

1) The Fundamental Theorem of Algebra states that in an nth-degree polynomial, there are n zeroes at most, including those that are complex. Therefore, there are 6 zeroes in the function since it's a 6th-degree polynomial.

2) Reduce the polynomial and use the Zero Product Property:

[tex]0=6x^3+25x^2-24x+5[/tex]

[tex]0=(6x^2-5x+1)(x+5)[/tex]

[tex]0=(3x-1)(2x-1)(x+5)[/tex]

[tex]x_1=\frac{1}{3},x_2=\frac{1}{2},x_3=-5[/tex]

Sam needs a bowl to mix her punch. She has 2-cup bowl, and a 6-cup. What is the smallest bowl sam can use to make her punch?

Answers

Answer:

the 2 cup bowl

Step-by-step explanation:

it is literally the smallest bowl she can use at her disposal

Please help me answer this​

Answers

Answer:

1) 1:2          2) 3

3) 1:8         4) 2:7

5) 1:4         6) 3:7

7) 2:5         8) 3:11

9) 2:7         10) 4:7

11) 8:9        12) 7:11

13) 1:2        14) 3

15) 26:27   16) 1:40

17) 1:10       18) 1:100

19) 1000    20) 10

Step-by-step explanation:

who ever gives to correct answer I will mark the brainiest ​

Answers

Answer:

the answer is B

Step-by-step explanation:

on the Cartesian plane u have to think of the distance from both the positive and negative side

so 3 is 3 units from the origin and -6 is 6 units from the origin

Therefore the total length is 9 (3+6)

And B is the only answer which will give 9

I have 17 ones, 15 tens, and 7 thousands​

Answers

Answer:

You have 7,167

Step-by-step explanation:

If this was to be converted into a whole number, it would be:

7,167

3) A Jewelry artist charges $7.00 for each pair of earrings she sells. in 3 hours, she sells 15 pairs of
earrings. At that rate, how much money could she earn from selling earrings for 5 hours?

Answers

Answer: $175

Step-by-step explanation:

$7.00 x 15 = $105.00

$105.00 / 3 hours = $35/hr.

$35 x 5 = $175

WILL BRAINLIST IF YOU GET CORRECT AND HURRY
A pair of linear equations is shown below: y = −3x + 5 y = x + 2 Which of the following statements best explains the steps to solve the pair of equations graphically? (4 points)

A: On a graph, find the point of intersection of two lines, the first line has y-intercept = 5 and slope = −3, and the second line has y-intercept = 2 and slope = 1.

B: On a graph, find the point of intersection of two lines, the first line has y-intercept = −3 and slope = 5, and the second line has y-intercept = 1 and slope = 2.

C: On a graph, find the point of intersection of two lines, the first line has y-intercept = −5 and slope = 3, and the second line has y-intercept = −2 and slope = −1.

D: On a graph, find the point of intersection of two lines, the first line has y-intercept = 3 and slope = −5, and the second line has y-intercept = −1 and slope = −2.

Answers

ANSWER : B

I know cause I took it and it was B

Answer:

answer is b

Step-by-step explanation:

1. What is the definition of function?
answer choices (select all that apply)
a) Has inputs and outputs
b) Every input has only ONE output
c) X-values can repeat
d) x-values and y-values

Answers

It’s A B C and D
They are all correct

John types 265 words in 5 minutes. At this rate, how many words does he type per minute

Answers

Answer:

John can type 53 words per minute

Step-by-step explanation:

You would divide 265 by 5 to get the result of 53.

Answer: John types 53 words a minute

Step-by-step explanation:

1 We know he types 265 words in 5 minutes

2 DIvide 265 by 5 to get one minute

3 the answer is 53, so he types 53 WPM

can someone please help me i'm almost done with my work

Answers

Answer:

you are correct with the following question

The answer is D, you have the right one chosen

-
Point K is on line segment JL. Given JK = 3 and KL = 8, determine the length
JL.

Answers

Answer:

JL = 11 units

Step-by-step explanation:

Add the units between JK and KL together to get the answer for JL

11. Scott made 21 treat bags for his sister's birthday party. Each treat bag has the same
number of items inside. He used another 14 items after that. Write an expression to represent
the total number of items Scott used for the treat bags.

Answers

Answer:

21 x n + 14

Step-by-step explanation:

The number of items in each bag times the number of bags plus the 14 items.

a shape is made of 12 right triangles of equal size each right triangle has a base of 4 cm and a height of 5 cm what is the total area in square centimeter of the shape

Answers

Answer:

Step-by-step explanation:

The area  of a triangle is equal to half the product of its length (L) because of its height (h).

The base of the triangles is  

The height of the triangles is  

Then the area of one of the triangles is:

The figure is formed by 12 equal triangles, then the area of the figure  is:

What is the product of the expression below?
4/7

×
5/8

Answers

4/7 x 5/8
Multiply numerators and denominators

= 20 / 56
Simply

= 5 / 14

24 peppermint; 8 to 5

Answers

Five eighths of 24 is 15

I'll put this as random but you can answer it...
ill give yall 10 points if yall do it!

Answers

Answer: 4 gallons = 15 liters, 8 liters = 2 gallons, 12.5 liters = 3 gallons, and 6 gallons = 23 liters.

Answer:

yea no

Step-by-step explanation:

i really don't know sorry tho

What is the slope of the line?

Answers

Answer:

1/3

Step-by-step explanation:

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

m = (0- -3)/(5- -4)

m = 3/9 = 1/3

equations 50 - 3x = 110

Answers

Answer:

x = -20

Step-by-step explanation:

50 - 3x = 110

=> -3x = 110 - 50

=> -3x = 60

=> x = -20

Hoped this helped.

Step-by-step explanation:

50 - 3x = 110

3x = 110 - 50

3x = -60

x = -20

A mini cooper is 120 inches long. A truck is 83% longer than the car.
How long is the truck?

Answers

Answer:A 16-ounce can of mixed nuts includes 6 ounces of cashews and 10 ounces of almonds. What is the ratio of almonds to mixed nuts in this can of nuts?

Step-by-step explanation:

Answer:

705.8823529411765

Step-by-step explanation:

You find out what percent the Mini Cooper is a subtract that from the full 100%. You would then have 17%. Now you need to divide the 120 inches by 17 to find out what 1% equals. In this case 7.058823529411765, now you multiply by 100 to get the full 100%. The answer is 705.8823529411765

Please HELP Write the graph's domain and range in interval notation.

Answers

Step-by-step explanation:

Domain: x€ [ -7;7]

Range : y€ [-6;4]

For the domain, the graph's x-values are from -7 to 7

For the range, the graph's y-values are from -6 to 4

Food fryers manufactured by a company that supplies food trucks can fry a
mean of 132.4 pounds of food per hour with a standard deviation of 3.9
pounds per hour. In a given hour, how much food would 99.7% of these fryers
fry?
A. 124.6 pounds per hour to 140.2 pounds per hour
B. 128.5 pounds per hour to 136.3 pounds per hour
C. 120.7 pounds per hour to 144.1 pounds per hour
D. 116.8 pounds per hour to 148.0 pounds per hour

Answers

Answer:

Correct Answer is C. 120.7 pounds per hour to 144.1 pounds per hour.

Step-by-step explanation:

Just took the Quiz <3

Helppppppppppppppppppp

Answers

Answer:

<6

<4

Step-by-step explanation:

Remote interior angle is an interior angle that is not adjacent to the exterior angle of interest.

<6

<4

The height of a door is 1.8 feet longer than it's with its front area is 1496.9 ft.² find the width and height of the door

Answers

The width of the door is [tex]37.8ft[/tex] and the height of the door is [tex]39.6ft[/tex]

Let

[tex]A=\text{the front area of the door}\\h=\text{the height of the door}\\w=\text{the width of the door}[/tex]

From the question

[tex]A=w\times h=1496.9\\h=w+1.8[/tex]

We are to find both the width and the height of the door. To proceed, we have to eliminate the height, and solve for the width. Later, we calculate the value of the height from the width.

Eliminate the height;

[tex]A=w\times h\\A=w\times(w+1.8)\\w^2+1.8w-A=0[/tex]

substitute the value of the front area into the equation and solve for the width

[tex]w^2+1.8w-1496.9=0\\w\approx 37.8\text{ or }w\approx-39.6[/tex]

the width can only take positive value. Now, to get the height

[tex]h=w+1.8\\=37.8+1.8\\=39.6[/tex]

the width and height of the door are [tex]37.8ft[/tex] and [tex]39.6ft[/tex] respectively.

Another example can be found in the link: https://brainly.com/question/18625465

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