# TrigonometryProving trigonometric functions

#### kbr1804

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

#### skeeter

##### Well-known member
MHB Math Helper
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 $3\cos{x}$

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#### kbr1804

##### New member
yeah i think i got it lol thanks alotand yeah it was supposed to equal to 3cos2x that was a typo

#### jonah

##### Active member
Beer soaked ramblings follow.
How can i prove that 6cos(x+45) cos(x-45) is equal to 3cosx?
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 $3\cos{x}$
yeah i think i got it lol thanks alotand yeah it was supposed to equal to 3cos2x that was a typo
Three graphs; shouldn't 2 of them have the same graph?

#### skeeter

##### Well-known member
MHB Math Helper
show up the same on my calculator ...

and on Desmos ...

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#### Evgeny.Makarov

##### Well-known member
MHB Math Scholar
jonah, in Desmos one should write $\pi/4$ instead of 45.

#### skeeter

##### Well-known member
MHB Math Helper
jonah, in Desmos one should write $\pi/4$ instead of 45.
One can change to degree mode with the "wrench" button menu

#### jonah

##### Active member
Beer soaked ramblings follow.
jonah, in Desmos one should write $\pi/4$ instead of 45.
One can change to degree mode with the "wrench" button menu
Well aware of that.
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).
... and on Desmos ...

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.

#### Country Boy

##### Well-known member
MHB Math Helper
How can i prove that 6cos(x+45) cos(x-45) is equal to 3cosx?
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.

#### skeeter

##### Well-known member
MHB Math Helper
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 …

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 $3\cos{x}$