Mathematics High School

prove the following identity showing all steps:
[tex]\frac{cos(x+30)-sin(x+60)}{sin(x)cos(x)} =-sec(x)[/tex]

please help fast

Answers

Answer 1

Answer:

See solution below

Step-by-step explanation:

Given the expression

[tex]\frac{cos(x+30)-sin(x+60)}{sin(x)cos(x)} \\[/tex]

Recall that

cos x  = sin(90-x)

cos(x+30 ) = sin (90-(x+30)

= sin(90-x-30)

= sin(60-x)

Substitute

[tex]\frac{sin(60-x)-sin(x+60)}{sin(x)cos(x)} \\= \frac{sin60cosx-cos60sinx)-sinxcos60-cosxsin60)}{sin(x)cos(x)} \\= \frac{-2cos60sinx)}{sin(x)cos(x)} \\= \frac{-2(1/2)sinx)}{sin(x)cos(x)} \\= \frac{-1}{cos(x)}\\= \frac{1}{cos(x)}\\ \\= -sec(x) Proved[/tex]

Related Questions

The lengths of a triangle are given below. Is the the triangle obtuse, acute, or right?
7, 13, 16

Answers

Answer:

This is an Acute triangle because all 3 angles are less than 90

If a system of linear equations has an infinite number of solutions, what do you know about the graph of the system?

А. The lines intersect at one point.
В. The lines are parallel
C. The lines are the same line.
D. The lines cannot be graphed.

Answers

The answer is B because they never pass through each other therefore it has infinite possibilities

Eleanor placed some marbles in a bag for an experiment. She reaches into the bag and grabs a marble. Eleanor writes down the color of the marble and then places the marble back in the bag. This process is repeated 100 times. The marbles are either red, black, or gray. The probabilities of randomly choosing a marble of a given color are shown below.

Answers

Answer:

Hi I have this same question but I'm torn between certain and very likely it is on of those options.

Step-by-step explanation:

Do you like math? If you do solve this simple equations
[tex]2 + 2 + 4 + 4 + 8 + 8 + 16 + 16[/tex]
​

Answers

uhhh it’s 60, right?

Answer:

60 ?

Step-by-step explanation:

PLS HElp PLZZZZZZZZZZZZZZZZZZZ

Answers

Answer:

c

Step-by-step explanation:

they use multiples of 9

what expressions represent divide the difference of 27 and 6 by the difference of 12 and 9?

Answers

Answer:

27-6/12-9

Step-by-step explanation:

27-6/12-9

21/3=7

(27 - 6) ÷ (12 - 9)

(27 - 6) ÷ (12 - 9)

(27 - 6) ÷ (12 - 9)

please helpp will mark brainlyist

Answers

I’m pretty sure it’s (3.63)


3.631923997916374

For a beverage, Lisa mixes cups of lemonade to cups of iced tea in a ratio of 2:5. Which of the following best describes the amount of lemonade to iced tea?

For every 2 cups of lemonade, there are 3 cups of iced tea.
For every 2 cups of lemonade, there are 5 cups of iced tea.
For every 3 cups of lemonade, there are 2 cups of iced tea.
For every 5 cups of lemonade, there are 2 cups of iced tea.

Answers

Answer: for every 2 cups of lemonade there are 5 cups of tea

Step-by-step explanation:

For every 2 cups of lemonade, there are 5 cups of ice tea

help me please..............

Answers

Answer:

a.)48

b.)528

c.)448

Step-by-step explanation:

a.)8x8=64. 4x4=16 64-16=48

b.)48(from a. answer)x11=528

c.)11x8(x2 for the other side)=176. 11x4x4=176.

48x2=96. 176+176+96=448

The sum of two numbers is 90. Their difference is 18. Find
the numbers.

Answers

Answer:

54 and 36.

Step-by-step explanation:

please help asap I will make you brainliest and please don't put a link The area of the base of a triangular pyramid is 90 meters squared, and its height is 6 meters. The volume of a pyramid can be found using the formula V = one-third B h. Which expressions can be used to find the volume of the pyramid? Select three choices.

Answers

Answer:

I think It is the third and fifth.

Step-by-step explanation:

i do not know for sure though.


Will give brainpower if you show work

Answers

Answer:

full question is not visible..............

Answer:

We dont know the question

Step-by-step explanation:

In the XY coordinate plane, the slope of a line is 4 and it passes through the point (1,3). Find the equation of a line that is perpendicular to the given line and intersects it at the given point.
A. y=4x-1
B. y=-4x+7
C. y=1/4x -1
D. y=4x+13/4
E. y=-1/4x+13/4

Answers

Answer:

E?

Step-by-step explanation:

I'm sorry of this answer is wrong

How do you find the height of a cone without given volume? Radius is 9

Answers

Square the radius then divide the radius squared to three times the volume
Ex the radius is 2 the square is 2 4 , and 300 divided by 4 75 for height

help me please i dont understand parrelagrams

Answers

Answer:

rhombus

Step-by-step explanation:

is it multiple choice?

Answer:

parallelogram

Step-by-step explanation:

Your welcome!

Alyssa is a waitress at a restaurant. Each day she works, Alyssa will make a
guaranteed wage of $20, however the additional amount that Alyssa earns from tips
depends on the number of tables she waits on that day. From past experience, Alyssa
noticed that she will get about $15 in tips for each table she waits on. How much
would Alyssa expect to earn in a day on which she waits on 10 tables? How much
would Alyssa expect to make in a day when waiting on t tables?
Earnings for 10 tables:
Earnings for t tables:

Answers

Answer:

$170

20+15t

Step-by-step explanation:

she already makes $20 in a day and then you add the 10 times $15 in tips which makes 170.

for the equation, she makes 20 so you add it to 15 times t which is the hypothetical number of tables

Line p is parallel to line q. If the measure of angle 3 is 54 what is the measure of angle 6?... Help

Answers

Answer:

54°

Step-by-step explanation:

Because p and q are parallel, angle 3 equal to angle 6 as they are alternative angles.

So angle 6 is 54°.

Alternative

Line p and line q is parallel, so that the sum of a pair of interior angles (angle 3 and angle 5, angle 4 and angle 6) are equal to 180°.

So angle 4 + angle 6 = 180°.

Find angle 4 first:

180° - angle 3 = angle 4

180° - 54° = 126°

So the measure of angle 6 is

180° - 126° = 54°

Answer:

54 degrees

Step-by-step explanation:

Simplify x + 6–3x – 8.

Answers

download Photomath that should help
Answer: = -2(x+1)

Hope I understood that correctly, and hope it helps!

ive been stuck on problem 20 for so long, help!!

Answers

I believe it’s letter i.

What is the value of X

enter your answer in the

box X=

Answers

Answer:

What is the value of X I would say it is 52

2) Mr. Jenkins deposited $1,200 into an account. He made no additional
deposits or withdrawals. Jenkins earned 4.0% annual simple interest on
the money in the account. What was the balance in dollars and cents in
Mr. Jenkins's account at the end of 4 years?

Answers

Hello, I Am BrotherEye

Answer:

The balance in dollars and cents in Mr. Jenkins’s account at the end of 4 years was $ 1,462.50

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Initial deposit = $ 1,250

Interest rate = 4.25% annual simple = 0.0425

Time of investment = 4 years

2. What was the balance in dollars and cents in Mr. Jenkins’s account at the end of 4 years?

Let's recall the simple interest formula, as follows:

A = P * (1 + rt), where:

A = final amount

P = initial principal balance

r = annual interest rate

t = time (in years)

Replacing with the values we know:

A = P * (1 + rt)

A = 1,250 * (1 + 4 * 0.0425)

A = 1,250 * 1.17

A = 1,462.50

The balance in dollars and cents in Mr. Jenkins’s account at the end of 4 years was $ 1,462.50

Step-by-step explanation:

The Pony Express
Chapter 1
At A Nation's Crisis
The Pony Express was the first rapid transit and the first fost mail line across the continent from the Missouri River to the Pacific Coast. It was a system
by means of which messages were carried swiftly on horseback across the plains and deserts, and over the mountains of the far West It brought the
Adontic coost and the Pacific slope ten days nearer to each other.
It had a brief existence of only sixteen months and was supplanted by the transcontinental telegraph. Yet it was of the greatest importance in
binding the East and West together at a time when overland travel was slow and cumbersome, and when a great national crisis made the rapid
communication of news between these sections an imperative necessity.
The Pony Express marked the highest development in overland travel prior to the coming of the Pacific railroad, which it preceded nine years.
It, in fact, proved the feasibility of a transcontinental road and demonstrated that such a line could be built and operated continuously the year
around-a feat that had always been regarded as impossible.
The operation of the Pony Express was a supreme achievement of physical endurance on the part of man and his ever faithful companion, the
horse. The history of this organization should be a lasting monument to the physical sacrifice of man and beast in an effort to accomplish
something worthwhile. Its history should be an enduring tribute to American courage and American organizing genius.
Read this line from the Pony Express excerpt
It hod a brief existence of only sixteen months and was supplanted by the transcontinental telegraph.
Based on the corres, what does the word "supplanted" mean? (5 points)
Defeated
Joined
Replaced
Os
Oo
Unearthed

What is f(x)=2x-1 if x=0

Answers

Answer:

[tex]f=\frac{2x-1}{x}[/tex]

Step-by-step explanation:

A circular flower bed is 17m in diameter and has a circular sidewalk around it that is 2m wide. Find the area of the sidewalk in square meters. Use 3.14 for (pie sign).
The area of the sidewalk is (insert answer) m(squared)
​(Round to the nearest whole number as​ needed.)

Answers

Answer:53.38 is the answer

Step-by-step explanation:

The radius is always half of the diameter so half of 17 is 8.5. 8.5x3.14 is 26.69. Then you add 26.69+26.69 to get the answer. (I’m not positive that this is correct)

find the y intercepts and x
for 11, 12

Answers

11.

x= 5 and y= -6

12. x= -4 and y= -5

Answer:

11.

y-int: 3

x-int: -6

slope: 1/2

12.

y-int: -5

x-int: -4

slope: 1

there are two machines that can produce aluminum cans. The newer machine can produce 5400 cans in 180 minutes. It takes the older machine 217 minutes produce that many cans. If the two machines work together, how long will it take them to produce 5400 cans?

Answers

The newer machine works at a unit rate of

(5400 cans) / (180 min) = 30 cans/min

while the older machine operates at

(5400 cans) / (217 min) ≈ 24.88 cans/min

So working together, the two machines work at a rate of about 54.88 cans/min. Producing 5400 cans would then take about

(5400 cans) / (54.88 cans/min) ≈ 98.39 min

Any help is appreciated. 10 points.

Answers

3*7 = 21 so the second answer is the right one
C not sure ?????????????

A number is added to ⅔ of itself.
If the same number is doubled,
write down the final expression.​

Answers

Answer:

4/3

Step-by-step explanation:

⅔ + ⅔ = 4/3

-33 = -18 + b

i also need the work for it

Answers

Answer:

Solution given:

-33 = -18 + b

b=-33+18=-15

b=-15 is your answer

what is the 2nd term of the linear sequence below?
13,7,1,-5,-11​

Answers

7 would be the second term. input that in the equation using a formula. If not then 7 is your answer

Add and subtract fractions word problems

Answers

Answer: Jessica ate 3/10 of the pizza

Step-by-step explanation:

We know that combined, Lulu and Jessica ate 7/10 of a pizza. Since we are given that Lulu at 4/10 of the pizza, we subtract 4/10 from 7/10. Because the denominators are the same, we can easily subtract without any extra step. 7/10 - 4/10 = 3/10

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