- #1

kbr1804

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How can i prove that 6cos(x+45) cos(x-45) is equal to 3cosx?

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- MHB
- Thread starter kbr1804
- Start date

In summary, the conversation discusses how to prove that $6\cos(x+45)\cos(x-45)$ is equal to $3\cos(2x)$, not $3\cos{x}$. The use of the sum/difference identity for cosine is mentioned and a typo is pointed out. Additional discussion on graphing this equation on Desmos is also included.

- #1

kbr1804

- 2

- 0

How can i prove that 6cos(x+45) cos(x-45) is equal to 3cosx?

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- #2

skeeter

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- 1

use the sum/difference identity $\cos(a \pm b) = \cos{a}\cos{b} \mp \sin{a}\sin{b}$

it should be equal to $3\cos(2x)$, not $3\cos{x}$

it should be equal to $3\cos(2x)$, not $3\cos{x}$

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- #3

kbr1804

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yeah i think i got it lol thanks alot:)and yeah it was supposed to equal to 3cos2x that was a typo

- #4

jonah1

- 107

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kbr1804 said:How can i prove that 6cos(x+45) cos(x-45) is equal to 3cosx?

skeeter said:

it should be equal to $3\cos(2x)$, not $3\cos{x}$

Three graphs; shouldn't 2 of them have the same graph?kbr1804 said:yeah i think i got it lol thanks alot:)and yeah it was supposed to equal to 3cos2x that was a typo

https://www.desmos.com/calculator/x3dyyfbucy

- #5

skeeter

- 1,103

- 1

show up the same on my calculator ...

and on Desmos ...

[DESMOS]{"version":7,"graph":{"viewport":{"xmin":-180,"ymin":-10.762090536086637,"xmax":180,"ymax":10.762090536086637},"degreeMode":true,"squareAxes":false},"randomSeed":"78931067dd5aa2f77a194c669752ab59","expressions":{"list":[{"type":"expression","id":"1","color":"#c74440","latex":"6\\cos\\left(x+45\\right)\\cos\\left(x-45\\right)\\left\\{x>0\\right\\}"},{"type":"expression","id":"2","color":"#2d70b3","latex":"3\\cos\\left(2x\\right)\\left\\{x<0\\right\\}"},{"type":"expression","id":"3","color":"#388c46"}]}}[/DESMOS]

and on Desmos ...

[DESMOS]{"version":7,"graph":{"viewport":{"xmin":-180,"ymin":-10.762090536086637,"xmax":180,"ymax":10.762090536086637},"degreeMode":true,"squareAxes":false},"randomSeed":"78931067dd5aa2f77a194c669752ab59","expressions":{"list":[{"type":"expression","id":"1","color":"#c74440","latex":"6\\cos\\left(x+45\\right)\\cos\\left(x-45\\right)\\left\\{x>0\\right\\}"},{"type":"expression","id":"2","color":"#2d70b3","latex":"3\\cos\\left(2x\\right)\\left\\{x<0\\right\\}"},{"type":"expression","id":"3","color":"#388c46"}]}}[/DESMOS]

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- #6

Evgeny.Makarov

Gold Member

MHB

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- #7

skeeter

- 1,103

- 1

Evgeny.Makarov said:jonah, in Desmos one should write $\pi/4$ instead of 45.

One can change to degree mode with the "wrench" button menu

- #8

jonah1

- 107

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Evgeny.Makarov said:jonah, in Desmos one should write $\pi/4$ instead of 45.

Well aware of that.skeeter said:One can change to degree mode with the "wrench" button menu

Force of habit.

In the absence of the degree symbol (°), assumed that 45 was in radians.

Didn't occur to me to check it in degree mode.

Usually do it by multiplying the degree measure by $\frac{\pi}{180}$ if the expression just gives it once. Otherwise, I usually do it by skeeter's suggestion (which I'm also quite aware of).

I've often wondered what kind of platform this type of Desmos "quoting" is ever since I saw one of Klaas van Aarsen's post which used the same method. It isn't just a link to Desmos as I found out when I hit the reply tab on my phone. Is it that the TikZ thingamajig I've been seeing a lot lately on this site? I think I remember copying that stuff in another math site but was surprised that it didn't work there.skeeter said:... and on Desmos ...

[DESMOS]{"version":7,"graph":{"viewport":{"xmin":-180,"ymin":-10.762090536086637,"xmax":180,"ymax":10.762090536086637},"degreeMode":true,"squareAxes":false},"randomSeed":"78931067dd5aa2f77a194c669752ab59","expressions":{"list":[{"type":"expression","id":"1","color":"#c74440","latex":"6\\cos\\left(x+45\\right)\\cos\\left(x-45\\right)\\left\\{x>0\\right\\}"},{"type":"expression","id":"2","color":"#2d70b3","latex":"3\\cos\\left(2x\\right)\\left\\{x<0\\right\\}"},{"type":"expression","id":"3","color":"#388c46"}]}}[/DESMOS]

- #9

HOI

- 921

- 2

You CAN'T- it's not true! For example if x= 45 degrees this becomes 6 cos(90)cos(0)= 6(0)(1)= 0 but 3 cos(45)= 3sqrt(2)/2.kbr1804 said:How can i prove that 6cos(x+45) cos(x-45) is equal to 3cosx?

- #10

skeeter

- 1,103

- 1

Country Boy said:You CAN'T- it's not true! For example if x= 45 degrees this becomes 6 cos(90)cos(0)= 6(0)(1)= 0 but 3 cos(45)= 3sqrt(2)/2.

post #2 …

skeeter said:

it should be equal to $3\cos(2x)$, not $3\cos{x}$

Trigonometric functions are mathematical functions that relate the angles of a triangle to the lengths of its sides. The most commonly used trigonometric functions are sine, cosine, and tangent.

Proving trigonometric functions allows us to understand the relationships between angles and sides in a triangle and use them to solve complex geometric problems. It also helps to verify the accuracy of mathematical calculations involving trigonometric functions.

The most common methods used to prove trigonometric functions are the unit circle method, the right triangle method, and the algebraic method. These methods involve using geometric principles, trigonometric identities, and algebraic manipulations to prove the desired function.

Some common trigonometric identities used in proving functions include the Pythagorean identities, the double angle identities, and the sum and difference identities. These identities help to simplify complex trigonometric expressions and establish relationships between different functions.

Yes, some tips for proving trigonometric functions include understanding the properties of triangles, memorizing key identities, and practicing with different types of problems. It is also important to carefully follow the steps of the chosen method and double-check the solution for accuracy.

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