Prove that sin^4x + cos^4x= sinxcosx

Answers

Answer 1

Answer:

(the relation you wrote is not correct, there may be something missing, so I will simplify the initial expression)

Here we have the equation:

[tex]sin^4(x) + cos^4(x)[/tex]

We can rewrite this as:

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

Now we can add and subtract cos^2(x)*sin^2(x) to get:

[tex](sin^2(x))^2 + (cos^2(x))^2 + 2*cos^2(x)*sin^2(x) - 2*cos^2(x)*sin^2(x)[/tex]

We can complete squares to get:

[tex](cos^2(x) + sin^2(x))^2 - 2*cos(x)^2*sin(x)^2[/tex]

and we know that:

cos^2(x) + sin^2(x) = 1

then:

[tex]1 - 2*sin(x)^2*cos(x)^2[/tex]

This is the closest expression to what you wrote.

We also know that:

sin(x)*cos(x) = (1/2)*sin(2*x)

If we replace that, we get:

[tex]1 - \frac{sin^2(2*x)}{2}[/tex]

Then the simplification is:

[tex]cos^4(x) + sin^4(x) = 1 - \frac{sin^2(2*x)}{2}[/tex]


Related Questions

the area of 1.25 and 0.8

Answers

Answer:

2.05

Step-by-step explanation:

1.25 + 0.8= 2.05 but if your doing multiplication then it would be 1 just 1.

Write the equation in standard form.
y+ 7= -3/2 (x+1)

Answers

Answer:

2y + 3x = -17

Step-by-step explanation:

standard form is Ax + By = C

first step is to distribute -3/2 among 'x' and then by 1 to get:

-3/2x - 3/2

you now have y + 7 = -3/2x - 3/2

we want to get the -3/2x term on the same side as 'y' and get 7 from the right side to the left side

we want to add 3/2x to the left side of the equation because it is being subtracted:

y + 3.2x + 7 = -3/2

now we want to subtract 7 to the right side because it is currently being added:

y + 3/2x = -7 3/2

we can convert -7 3/2 to be -17/2

we now can eliminate the denominator of 2 in the 'x' term by multiplying each term by 2 to get:

2(y + 3/2x) = -17/2(2)

distribute and simplify to get:

2y + 3x = -17

Please help me ASAP!!!!!

Answers

Answer:

c and b

Step-by-step explanation:

behdjdurjnrnrjdjdjdi

c and b look pretty similar

I need help with this problem, if someone could help me? Please don't guess I really need to understand this algebra.

Answers

Hi, sir or ma'am, you said you needed help but you provide no information on what to help you with, no picture or anything.

Answer:

You need to upload an image of what you are talking about

Step-by-step explanation:

Walmart sells a 40-ounce jar of peanut butter for $5.58
What is the Unit Price?

Answers

The unit price is 0.20¢ per ounce.
To find the unit price, you divide the total price by the number of items, and in this case, you divide the total price by ounces

Find seven ordered pairs to the equation y=8 - x2.

NEED IT ASAP PLEASE!!!

Answers

-3   |  9-8=1       | (-3, 1)

-2   | 4-8= -4      | (-2, -4)

-1   | 1-8=-7       | (-1, -7)

0.  | 0-8=-8       |  (0, -8)

1   | 1-8=-7       |  (1, -7)


easiest way is just pick some small simple integers for x and plug it into the equation to find y

(0,-8)
(1,-7) 1^2-8 = -7
(2,-4) 2^2-8 = 4-8 = -4
(3,1) etc.
(4,8)
(5,17)
(6,28)

Just tell me which one it is because I am confused please help me

Answers

Answer:

[tex]d \: is \: correct[/tex]

Answer:

a. y = -2x-5

Step-by-step explanation:

*Don't get confused the y-axis scale is 2

I guess you would kind of have to guess by looking at the graph for this one, the y-intercept is 5.

The graph is negative because it is pointing the opposite way

The slope is 2 because the y-axis has a scale of 2

With these facts you can formulate that the equation would be y = -2x-5

Hayden has 7 shells . Elly has 5 fewer shells than Hayden . Beth has 2 shells . How many shells do they have in all?

Answers

Answer:

11 i think

Step-by-step explanation:

someone help i’ll mark brainliest!!! Find the equation of the line through (7,1)
that has a slope of 1/2
Express your answer in General (Standard) Form.

Answers

Answer:

y=1/2x - 2.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

We can use the point-slope formula to write an equation for this line. The point-slope formula states :

where m  is the slope and (x1   y1)  is a point the line passes through .

We can substitute the slope and values from the point to give:

(y-1) = 8 (x-7)

We can also transform this equation to the slope-intercept form by solving for  

y

. The slope-intercept form of a linear equation is: y=mx+b

where the m is the slope and b s the y-intercept value.

y-1= (8 times x) - ( 8 times 7)

y-1=   8x - 56

y-1 + 1= 8x- 56 + 1

y-0=  8x- 55

y= 8x - 55

18/3=????????????????????

Answers

[tex] \frac{18}{3} = 6[/tex]

When the values are given in upon they are supposed to be divided.

Answer:

18/3=6

Step-by-step explanation:

3 can be made out of 18 6 times

Given the matrices A and B shown below, solve for X in the equation -3X + A= 3B. ​

Answers

Answer:

A = 3 B + 3x

B = - X + A/3

Step-by-step explanation:

X = - B + A/3

I need help asaapppp

Answers

32 divided by 7 is 4.57

Mao counts by fives to 30.alana counts by tens to 40.who will say more numbers? Explain

Answers

Answer:

Mao will say more numbers

Step-by-step explanation:

Mao will say more numbers because, to get to 30, you must count by fives 6 times. For example, 5,10,15,20,25,30. There are 6 numbers there. On the contrary, Alana is only going to count 4 times. 10,20,30,40. 6 is greater than 4, therefore Mao will say more numbers. I hope this helps!

Amelia's garden is 7 feet long and 8 feet wide. What is the area of Amelia's garden?

Answers

Answer:

10 feet long each because 8 × .25 is 2 and 8 + 2 is 10

Step-by-step explanation:

Brainliest?

Please help me ASAP

Answers

the answer should be A

What is the equation of this line?

y=3/4x+2

y=4/3x−2

y=3/4x−2

y=−3/4x−2

Answers

Answer:

We need the picture

Step-by-step explanation:

Answer:

Step-by-step explanation:

Where's the line?

Is this correct now?

Answers

I would say no it’s not correct, the point is not in the correct place

Alex and her friends went out to lunch at the diner. The bill for lunch was $34.56 which included an 8% sales tax. How much was the price of the lunch before tax? ​

Answers

Answer:

34.48

Step-by-step explanation:

8% as a decimal is 0.08

34.56 - 0.08 = 34. 48

Prove the polynomial identity.

(4x^2−2)^2−(4x^2)^2=4(1−2x)(1+2x)
Drag and drop the lines of the proof in the correct order to complete the proof.

Answers

Answer:

(4x^2 - 2)^2 - (4x^2)^2 = 4(1 - 2x)(1 + 2x)

16x^4 - 16x^2 + 4 - 16x^4 = 4(1 - 2x)(1 + 2x)

4 - 16x^2 = 4(1 - 2x)(1 + 2x)

4(1 - 4x^2) = 4(1 - 2x)(1 + 2x)

4(1 - 2x^2)(1 + 2x) = 4(1 - 2x)(1 + 2x)

please help!
The freezing point of seawater is -2 °C. The freezing
point of nitric acid is -42 °C. How much greater is the freezing
point of seawater than the freezing point of nitric acid?

Answers

Answer:

Express concentrations of solution components using mole fraction and molality

Describe the effect of solute concentration on various solution properties (vapor pressure, boiling point, freezing point, and osmotic pressure)

Perform calculations using the mathematical equations that describe these various colligative effects

Describe the process of distillation and its practical applications

Explain the process of osmosis and describe how it is applied industrially and in nature

Step-by-step explanation:

i helped

GE bisects angle DGF , m angle DGE = 53º. Find m angle DGF.

M angle DGF

Answers

Answer:

4.5 degres

Step-by-step explanation:

Eraph the line that represents the equation Y = -2/3x + 1
I need answer ASAP

Answers

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

The equation is given in "slope-intercept" form.

  y = mx + b

where m is the slope, and b is the y-intercept.

__

For graphing, it is usually convenient to start with the y-intercept. The value of 'b' in your equation is +1, so the graph will go through the point y=1 on the y-axis. That point's coordinates are (0, 1).

The value of m represents the slope, or "rise"/"run" of the line. A slope of -2/3 means the line "rises" -2 units for each "run" of 3 units to the right. Then another point on the graph will be 3 units to the right of the y-axis, and 2 units down from y = 1. That point is (3, -1).

The line is drawn through these points you found on the graph.

divide 4x+2x^3+7x^2-1 by x=-1

Answers

Answer:

12

Step-by-step explanation:

4(1)+2(1)”3+7(1)”2-1

4+2+7-1

12

wait if x=-1 it’s zero

PLEASE HELP ME AND HURRY TOO NO LIBKS PLEASE I WILL GIVE BRAINLIEST

Answers

first one is denominator, then opposite of denominator.. i would wait for someone else to answer. but i’m pretty sure that’s correct. sorry if it is incorrect.. good luck on the rest of your assessment!!

What is the distance between the points (15,17) and (15,-4) in the coordinate plane?
A.
21 units
B.
10.5 units
C.
13 units
D.
2 units

Answers

Answer:

21

Step-by-step explanation:

15-15=0

17-(-4)=21

sqrt(0^2+21^2)=21

(b) A number increased by -8 is greater than 12

Answers

Answer:

x+-8 > 12 Hope this helps.

7/8 divided by 3/4 is what?

Answers

Answer:

1/8

Step-by-step explanation:

3/4=6/8

7-6=1

therefore 1/8

Answer:

7/6

Step-by-step explanation:

7/8 divided by 3/4= 7/8 x 4/3 = 28/24= 7/6

f(x) = x² + 2ax + a² - a
g(x) = 4 - x²

Let variable a be a real number. Find the range of values of a such that the equation f(x) = g(x) has two different solutions.

***The answer should be -2 < a < 4, but I don't know why.

Answers

Step-by-step explanation:

f(x) = x² + 2ax + a² - a

g(x) = 4 - x²

f(x) = g(x)

x² + 2ax + a² - a = 4 - x²

2x²+2ax+a²-a -4 =0

the equation has two different solutions

=> (2a)² - 4(2)(a²-a-4) > 0

4a²-8a²+8a +32 >0

-4a²+8a+32 > 0

a²-2a-8 >0

(a-4)(a+2) < 0

the answer should be

-2 < a < 4

Solve four-tenths plus four ninths

Answers

Answer:

[tex]\frac{38}{45}[/tex]

Step-by-step explanation:

[tex]\frac{4}{10} +\frac{4}{9}[/tex]

So first you need to have a common denominator (the number on the bottom)

The least common denominator (LCD) would be 90.

So then the fractions would be: [tex]\frac{36}{90} +\frac{40}{90}[/tex].

Add.

You get: [tex]\frac{76}{90}[/tex]

Simplify and the answer is [tex]\frac{38}{45}[/tex]

6. What is the value of x in the solution to the systems of linear equations shown below?
2x - 2y+z=3
5y-z= -31
x+ 3y + 2z = -21

Answers

Step-by-step explanation:

[tex]1) \: \: 2x - 2y + z = 3 \\ 2x = 3 + 2y - z \\ x = \frac{3 + 2y - z}{2} \\ \\ 2) \: \: \: not \: any \: \: \: x \: \: \: available \: \: \\ \\ 3) \: \: x + 3y + 2z = - 21 \\ x = - 21 - 3y - 2z[/tex]

Answer:

x= -5

Step-by-step explanation:

5y-z= -31, add z and 31 to both sides

5y+31 = z, substitute z in the other two given equations

2x - 2y+z=3

2x-2y +5y+31 = 3, combine like terms and subtract 31 from both sides

2x+3y = -28

x+ 3y + 2z = -21

x+3y +2(5y+31) = -21, distribute 2 over the addition parenthesis

x+3y +10y+62 = -21, combine like terms and subtract 62 from both sides

x+13y = -83

Now we have 2 equations  with 2 variables x and y to solve

2x+3y = -28

x+13y = -83

Because we need to find x then from the first equation we can write that

3y = -2x-28, subtract 2x from both sides and the divide both sides by 3

y = (-2x-28)/3, substitute this in the second equation

x + [13(-2x-28)/3] = -83 , distribute 13 . over the subtraction parenthesis

(3x/3)+[(-26x - 364) /3= -83, find the common denominator

3x+[(-26x - 364) = -83*3 , cross multiply

3x -26x = -249 +364, add 364 to both sides

- 23x = 115, divide both sides by (-23)

x= -5

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