Cos3x=4cos^3x-3cosx prove

Answers

Answer 1

Answer: $\bf cos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta)\n\n\n\textit{also recall that }cos(2\theta)=\begin{cases}cos^2(\theta)-sin^2(\theta)\n1-2sin^2(\theta)\n\boxed{2cos^2(\theta)-1}\end{cases}\n\n\nand\qquad sin^2(\theta)+cos^2(\theta)=1\implies sin^2(\theta)=1-cos^2(\theta)\n\n-------------------------------$

$\bf cos(3x)=4cos^3(x)-3cos(x)\n\n-------------------------------\n\ncos(3x)\implies cos(2x+x)\implies cos(2x)cos(x)-sin(2x)sin(x)\n\n\n\[2cos^2(x)-1]cos(x)-[2sin(x)cos(x)]sin(x)\n\n\n2cos^3(x)-cos(x)~~~~-~~~~2sin^2(x)cos(x)\n\n\n2cos^3(x)-cos(x)~~~~-~~~~2[1-cos^2(x)]cos(x)\n\n\n2cos^3(x)-cos(x)~~~~-~~~~[2cos(x)-2cos^3(x)]\n\n\n2cos^3(x)-cos(x)~~~~-~~~~2cos(x)+2cos^3(x)\n\n\n4cos^3(x)-3cos(x)$

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The Venus flytrap closes in 0.3 second and the waterwheel plant closes in 0.2 second what decimal in halfway between 0.2 and 0.3 ?

Answers

In order to find the number in between two numbers you need to calculate their mean. This can be done by adding them up then dividing by 2. In this case, 0.2+0.3 = 0.5. You can then divide this by 2 to give 0.25
Thus the decimal in between 0.2 and 0.3 is 0.25.

Hamid has gained weightHe now weighs 88kg, which is 10% higher than his normal weight.

What is Hamid's normal weight?

Answers

If we let x be Hamid's normal weight, 10% of the normal weight can be expressed as 0.10x. The equation that would let us better visualize the problem,
(1.10)x = 88

The value of x from the equation is 80.

Therefore, the answer is 80 kg.

The normal weight of Hamid is 80 kg.

Step-by-step explanation:

Given information:

The current weight of Hamid is 88 kg.

Let , $W$ is the normal weight of hamid.

Now , if he is having 10% extra weight

So,

The value 88 is sum of normal weight and 10% of the normal weight

So,

$W+0.10* W=88\n1.10* W=88\nW=80$

Hence, the normal weight of Hamid is 80 kg.

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Describe the translation of Point A (3, -8) to A'(-4,-5).

Answers

The translation path of Point A (3, -8) to A'(-4,-5) exists 3 units down and 7 units to the left.

What is meant by translation?

A translation in mathematics does not turn, but rather moves a shape left, right, up, or down. Congruent translations are those in which the translated shapes (or the image) seem to be the same size as the source ones. Just one or more directions have they shifted.

Each point in a figure is moved by the same amount and in the same direction during a translation, a type of transformation.

With a sort of transformation called translation, every point in a figure is moved the same distance in the same direction.

The translation path of Point A (3, -8) to A'(-4,-5) exists 3 units down and 7 units to the left.

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Answer:

left 7 and up 13

Step-by-step explanation:

A tent is in the shape of a triangular prism. The front and back are isosceles triangles with base 6 feet and height 4 feet. The surface area of the entire tent is 104 square feet. What is the depth of the tent?

Answers

If surface area of the entire tent is 104 square feet then the depth of the tent is approximately 4.44 feet.

What is Three dimensional shape?

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

The tent can be divided into three rectangular faces and two triangular faces. Let the depth of the tent be denoted by "d".

The area of each triangularface is (1/2) base x height = (1/2) x 6 x 4 = 12 square feet.

The area of each rectangular face is length x width = d x 6 feet.

Therefore, the total surfacearea of the tent is:

2 x 12 square feet (for the triangular faces) + 3 x (d x 6 feet) square feet (for the rectangular faces) = 24 + 18d

We know that the total surface area of the tent is 104 square feet, so:

24 + 18d = 104

Subtract 24 from both sides.

18d = 80

Divide both sides by 18.

d = 80/18 ≈ 4.44 feet

Therefore, if surface area of the entire tent is 104 square feet then the depth of the tent is approximately 4.44 feet.

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the depth is 5 feet of the tent

Hlelp plaese i made tpyos cuz i stresesd

Answers

If the veterinarians at Aquarian feed the zebrafish 7 pounds of food each day for 17 days, they would have used a total of 119 pounds of food. Therefore, the amount of food left over would be 5 pounds .

Step-by-step explanation:

7 x 17 = 119

124 - 119 = 5

Answer:

Solve the equation. –x + 8 + 3x = x – 6

Answers

First group the coefficients together on their side of the equal sign.
-x + 3x = 2x.

Then, since it is a positive number, subtract it from that side and the other side.

On the other side, the x becomes -x.

Add the 6 from the other side to the 8 to make 14.

14 = -x

Divide both sides by -1, to get the answer.

x = -14

-x+8+3x=x-6
8+2x=x-6
+6 +6
14+2x=x
-2x -2x
14/-1=-x/-1
-14=x

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