Prove the trigonometric identity!

Please help!! 50 Points!

Prove The Trigonometric Identity!Please Help!! 50 Points!

Answers

Answer 1

Answer:

:)

Step-by-step explanation:

For simplicity I will substitue [tex]x[/tex] for β.

[tex]1-sin(2x)=(cosx-sinx)^2\\1-2sin(x)cos(x)=cos^2x-2sin(x)cos(x)+sin^2x\\1=cos^2(x)+sin^2(x)\\1=1[/tex]

In the first step I used the identity

[tex]sin(2x)=2sin(x)cos(x)[/tex]

And I factored out [tex](cosx-sinx)^2[/tex]

Then it's just simple algebra to cancel till the 3rd step where we used another identity derived from the Pythagorean Theorem.

[tex]cos^2(x)+sin^2(x)=1[/tex]

That's it!


Related Questions

If the radius of the circle below is 12 feet, find the area of the shaded region.

Answers

If the radius of the circle below is 12 feet is given then the area of the circle would be 452.16 ft square.

What is the area of the circle?

The area of the circle is defined as the product of the pie and the square of the radius.

The area of the circle = [tex]\pi r^{2}[/tex]

If the radius of the circle below is 12 feet is given then

The area of the circle = [tex]\pi r^{2}[/tex]

 [tex]\pi 12^{2} \\\\3.14 \times 144\\\\452.16[/tex]

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All four triangles are similar, and two of the triangles are also congruent to each other. Drag the correct unit side lengths and angle measures to te corresponding boxes. Note that some values may be approximate.

Answers

Answer:

Step-by-step explanation:

I get everything correct

Write the algebraic expression that matches each graph.
(WILL GIVE BRAINLIEST!)

Answers

Answer:

y=11

Step-by-step explanation:

Let Vector f = LeftAngleBracket 4, 3, 7 RightAngleBracket. and Vector g = LeftAngleBracket negative 1, 0, 2 RightAngleBracket. . Which graph shows Vector f + vector g. ?

Answers

Vectors simply means a quantity that has both magnitude and direction but not position e.g acceleration.

What is a vector?

Your information is incomplete as the graphs aren't given. Therefore, an overview of vectors will be given.

In this case, vectors simply means a quantity that has both magnitude and direction but not position e.g acceleration, velocity, etc.

A vector can also be an element of the vector space. The direction is typically equal to the angle formed with the x-axis.

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NOTES
Lucia and Jack are training for a marathon. Lucia started the first day by running 2 miles and adds 0.25 mile to her distance every day, Jack
started the first day by running 0.5 mile and adds 0.5 mile to his distance every day. If both continue this plan, on what day will Lucia and
Jack run the same distance?

Answers

Answer:

Day 3

Step-by-step explanation:

2+0.25+0.25=2+0.50=2.50

0.5+0.5+0.5=2+0.5=2.5=2.50

they both run 2.50 miles on day three

The fox population in a certain region has an annual growth rate of 5 percent per year. It is estimated that
the population in the year 2000 was 28400.
(a) Find a function that models the population t years after 2000 (t = 0 for 2000).
Your answer is P(t)
=
(b) Use the function from part (a) to estimate the fox population in the year 2008.
Your answer is (the answer should be an integer)

Answers

Answer:

See below

Step-by-step explanation:

population =  28400* ( 1+.05)^t     t = years past 2000

8 years from 2000     pop = 28400(1.05)^8= 41 960 foxes

I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER

Answers

Answer:

use sine or cosine rule

Step-by-step explanation:

that's the answer by using the sine rule

Answer:

Step-by-step explanation:

Find the side length of a square with area 16/49 square inches

Answers

Answer: the correct answer is S= 4/7 inches.

The cost of gas increases monthly at a rate of 3.2%. If gas cost $1.75 today. How much will it cost in 3 years? ( round to the nearest cent (2 decimal places) )

Answers

Answer:

$1.92

Step-by-step explanation:

present cost = $1.75

time = 3 years

rate = 3.2%

cost after three years = present cost (1 +[tex]\frac{R}{100}[/tex] )^3

=$1.75 ([tex]\frac{103.2}{100}[/tex])^3

=$1.75*1.099

=$1.92

Threrefore , after 3 years cost of gas will be $1.92.

Question 7 of 10
How many different roots does the polynomial function, y = (x - 2)(+3)
have?
O A. 4
B. 3
O c. 2
O
D. 1
SUBMIT

Answers

c. 2

you should just get an app on ur phone its easier than asking here

Two different roots the given polynomial function have. Therefore, option C is the correct answer.

What is the solution of a quadratic equation?

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

The given equation is y=(x-2)(x+3)

The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace y with 0 and solve for x.

Here, (x-2)(x+3)=0

(x-2)=0 and (x+3)=0

x=2 and x=-3

Therefore, option C is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

How many different roots does the polynomial function, y = (x - 2)(x+3)?

A. 4

B. 3

C. 2

D. 1

The diameter of a circle is 20 m. Find the circumference to the nearest tenth.​

Answers

ANSWER: 62.83 m


explanation- c=2 pie

d=2r

c=pie d=pie • 20 = 62.83185 m

Answer:

about 62.8 meters

Step-by-step explanation:

[tex]c = 20\pi = 62.8[/tex]

Estimate the amount of the tip by rounding the bill to the nearest dollar before calculating.
15% tip on a bill of $41.58 The amount of the tip is approximately $

Answers

Answer:

Approximately $6.24

Step-by-step explanation:

You have to multiply 41.58 by 0.15 (basically 15%) and you have your answer.

I don't know the answer ccuh

Answers

Answer:

  minor arc

Step-by-step explanation:

This is a vocabulary question:

major arc: has a measure more than 180°minor arc: has a measure less than 180°semicircle: has a measure of exactly 180° (connects the ends of a diameter)

__

Arc EA is a minor arc.

_____

Additional comment

In general, unless the two named points are the ends of a diameter, the arc is a minor arc. A major arc will generally be defined by designating a third point on the long arc connecting the same points on the circumference. For example, EDA, ECA, and EBA all designate the major arc connecting points E and A. (We can also use the descriptor, "major arc EA.") Without any of these extras designating the major arc, EA is considered to be the minor arc.

If x is 6 and y is -2 what’s the value of yx

Answers

Answer:

-12

Step-by-step explanation:

(6)(-2)= -12

6 multiply -2 equals 12.

6x -3y -15 = 0 please solve for me

Answers

Step-by-step explanation:

Add 3y to both sides

6x-3y- 15 + 3y =0+3y

Simplify

6x- 15 =3y

Add 15 to both sides

6x-15 + 15 =3y + 15

Simplify

6x =3y+ 15

Divide both sides by6

6x/6= 3y/6+ 15/6

x=y+5/2

use this dataset for the next three questions: 5, 10, 12, 4, 6, 11, 13, 5 1. Calculate the mean. 2 Ultimate Medical Academy.
calculate the mean​

Answers

Answer:

11.8

Step-by-step explanation:

5 + 10 + 12 + 4 + 6 + 11 + 13 + 51= 118

The average (mean) is equal to the sum of all the data values divided by the count of values in the data set.

Count = 10

Sum = 118

Average = Sum / Count

118/10= 11.8

Question 13
You deposit $8,400 in an account earning 3.6% interest compounded monthly.
a. How much will you have in the account in 20 years?
b. How much interest will you earn?

Answers

Answer:

A = $17,238.65

I (interest) = $8,838.65

Step-by-step explanation:

Using the formula A = P(1 + r/n)^nt

A = $17,238.65

A = P + I where

P (principal) = $8,400.00

I (interest) = $8,838.65

First, convert R as a percent to r as a decimal

r = R/100

r = 3.6/100

r = 0.036 rate per year,

Then solve the equation for A

A = P(1 + r/n)^nt

A = 8,400.00(1 + 0.036/12)^(12)(20)

A = 8,400.00(1 + 0.003)^(240)

A = $17,238.65

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $8,400.00 at a rate of 3.6% per year compounded 12 times per year over 20 years is $17,238.65

what is the simplest form of 2/3 - 1/4 =

Answers

Answer:

I got 5/12

Step-by-step explanation:

Hope this helped

ANSWER

The answer will be

Step-by-step explanation:

5/2=0•416666667

3 Select the correct answer. How can you write the expression 7(b – 2) in words? A. two subtracted from the quotient of seven divided by b B. seven added to difference of b minus two C. the quotient of seven divided by b minus two D. two subtracted from seven times b E. the product of seven and the difference of b minus two

Answers

Answer:

option E is correct.

Step-by-step explanation:

from the options, the correct answer is:

the product of seven and the difference of b minus two.

HOPE THIS HELPSPLEASE RATE AND MARK BRIANLIEST!!!

please help this is urgent!!

Answers

Answer:

x=37 and scalene or right triangle

Step-by-step explanation:

Answer:

37°

Step-by-step explanation:

Any Triangle his total angles = 180

then: 53 + 90 + X = 180

then: X= 180 - (90+53)

= 37

The sum of two fractions is 2/3.
One fraction is 1/2.
What is the other fraction?

Answers

Answer:

0.5/3

Step-by-step explanation:

1/2 can be turned into 2/4, which means that to be 1/3, it has to be 1.5/3. 1.5/3 + 0.5/3 equals 2/3.

The other fraction would be 1/6.

NEED THIS ASAP
Which statement describes (²) ?
n=1
The series diverges because it has a sum of 1.
O The series converges because it has a sum of 1.
O The series converges because it has a sum of 4.
The series diverges because it does not have a sum.

Answers

Answer:

option b

please mark me as brainliest

Answer: the series converges because it has a sum of 1 (b)

Step-by-step explanation:

bec i said so

Use the shell method to write and evaluate the definite integral that represents the volume of the solid generated by revolving the plane region about the y-axis.
y = 3 − x

Answers

The volume of the solid generated by revolving the plane region y=3−x about the y-axis is 9π cubic units.

What is integration?

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

We have a function:

y = 3 - x

From the graph:

Shell radius = y

Height = 3 - y

From the shell method, we can write the integral as follows:

[tex]\rm Volume =2\pi\int\limits^0_{-3} {y(3-y)} \, dy[/tex]

[tex]\rm Volume =2\pi\int\limits^0_{-3} {(3y-y^2)} \, dy[/tex]

After solving the above definite integral, we will get volume:

Volume = 9π cubic units

Thus, the volume of the solid generated by revolving the plane region y=3−x about the y-axis is 9π cubic units.

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28 out of 35 students in ms. baileys class have older siblings. what percent of the class has older siblings

Answers

Answer:

80%

Step-by-step explanation:

We can get the percent value of the amount of students who have older siblings by diving 28 by 35.

28 / 35 = 0.8

We can convert this decimal into a percentage, giving us 80%.

Therefore, we know that 80% of the students in Ms. Bailey's class have siblings.

Find the volume of this shape. Show work and round to the nearest hundredth pls.

Answers

Answer:

V = 150.80 cu.ft.

Step-by-step explanation:

shape is a cone

[tex]V=\frac{1}{3} \pi r^{2} h[/tex]

[tex]r=8/2=4ft[/tex]

[tex]h=9ft[/tex]

Then:

[tex]V=\frac{1}{3} \pi (4)^{2} (9)=48\pi =150.80cu.ft[/tex]

Hope this helps

Can you crack the code?
One number is
correct and placed
well
2
6
5
Nothing is right
3
8
7
One number is correct but wrongly placed
2
3
4
Two numbers are correct but wrongly placed
4
7
1
The numeric logic has a digit of
?
?
?

Answers

Answer:

1,2,4 is the correct answer

hope it'll help you out

What is the volume of this object?
__u3

Answers

Answer:

15u³

Step-by-step explanation:

To find volume ↓

Volume

= length × width × height

= 2u × 2½u × 3u

= 15u³

Hope this helps =)

A circular flower garden surrounds a sculpture on a square base as shown. What is an expression for the area of the flower garden?
The number from the center of the square is 6x and the flower garden area is 4x

Answers

The given object is made up of circle and squares. The expression for the area of the flower garden is 4π²(9π - 4)square units

Area of composite object

The given object is made up of circle and squares. To find the area of the garden, we wil use the expression

Area of the garden = area of circle - area of square

Find the area of circle

Area = πr²

Area = π(6π)²

Area pf circle = 36π³ square units

For the square

A = length * length

A = 4²π²

A = 16π²square units

Take the difference

D =   36π³ - 16π²

D =4π²(9π - 4)square units

Hence the expression for the area of the flower garden is 4π²(9π - 4)square units

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Answer: (pi * r^2) - (6x*4x)

Step-by-step explanation:
Since the formula of the area of a circle is pi * r^2 and the area of a square is base* height or in this case 6x*4x the answer is: (pi * r^2) - (6x*4x). The reason we subtract is because your trying to find the area of the square inside the circle.

A whole number is squared. The result is between 200 and 260. The number is between:
A) 10 and 11
B) 15 and 16
C) 13 and 14

Answers

Answer:

B

Step-by-step explanation:

b is correct

A pizza dough recipe has a ratio of 5 cups of flour to 2 cups of water. There are ?
cups of flour per cup of water

Answers

Answer:

2.5 cups of flour per cup of water.

Step-by-step explanation:

We can divide the entire recipe by two, to get the amount of flour to 1 cup of water.

5/2 = 2.5

2/2 = 1

Therefore, 2.5 cups of flour needs 1 cup of water.

Answer:

There are 2.5 cups of flour per cup of water

Step-by-step explanation:

Step 1:  Find the ration

Cups of Flour : Cups of Water

5 : 2

2.5 : 1

Answer:  There are 2.5 cups of flour per cup of water

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