Welcome to our community

Be a part of something great, join today!

Trigonometry Proving trigonometric functions

kbr1804

New member
Oct 6, 2021
2
How can i prove that 6cos(x+45) cos(x-45) is equal to 3cosx?
 

skeeter

Well-known member
MHB Math Helper
Mar 1, 2012
1,013
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 $3\cos{x}$
 
Last edited:

kbr1804

New member
Oct 6, 2021
2
yeah i think i got it lol thanks alot:)and yeah it was supposed to equal to 3cos2x that was a typo
 

jonah

Active member
Feb 21, 2015
109
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 alot:)and 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
Mar 1, 2012
1,013
show up the same on my calculator ...

trig_eqs.png
trig_grafs.png

and on Desmos ...

 
Last edited:

Evgeny.Makarov

Well-known member
MHB Math Scholar
Jan 30, 2012
2,547
jonah, in Desmos one should write $\pi/4$ instead of 45.
 

skeeter

Well-known member
MHB Math Helper
Mar 1, 2012
1,013

jonah

Active member
Feb 21, 2015
109
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.