#Trig identity help

99 messages · Page 1 of 1 (latest)

spice fjord
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Verified it's equivalent, not sure of steps

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celest quartzBOT
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wheat lionBOT
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wolfqz

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versed bay
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@spice fjord

spice fjord
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oh there's wolfram alpha in here?

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texit*

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great

versed bay
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yeah

spice fjord
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so all you did was simplify the 2's

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what goal would that serve though

wheat lionBOT
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wolfqz

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versed bay
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wait no lemme recheck just a sec

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yeah no we cant prove it

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the things arent equivalent to start with

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they only share the same zeroes

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wait let me use desmos to graph them

spice fjord
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,w (sqrt2/2 cosx- sqrt2/2 sinx)/(sqrt2/2 cosx+ sqrt2/2 sinx)=tan(pi/4 -x)

wheat lionBOT
spice fjord
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it should be true

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because LS is what I had, multiplied by 2sqrt2 on both sides to eliminate the roots

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RS is the other side of my identity

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which means if this holds true then the identity does

versed bay
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,w (cos x - sin x)/(cos x + sin x) = (cos (2x))/(1+sin(2x))

wheat lionBOT
versed bay
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oh that means

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okay wait

gilded orchid
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May i try

versed bay
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i got it now but sure

gilded orchid
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You can multiply divide by sinx+cosx

versed bay
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$\frac{\cos x - \sin x}{\cos x + \sin x} = \frac{(\cos x - \sin x)^2}{\cos^2x-\sin^2x}$

gilded orchid
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On top you get cos²x-sin²x

wheat lionBOT
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wolfqz

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gilded orchid
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Mm no

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I told sinx+cos x

versed bay
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nah it works

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trust me bro

gilded orchid
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Ok

spice fjord
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I'm confused on how multiplication even happens

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are you multiplying both sides by cosx-sinx

versed bay
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yeah

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$\frac{\cos^2 x + \sin^2 x + 2\sin x\cos x}{\cos(2x)}$

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WHAT

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how did i get the reciprocal

gilded orchid
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I told

spice fjord
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😂

gilded orchid
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Multiply by +

spice fjord
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your on the right track

gilded orchid
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Not -

versed bay
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,rotate

wheat lionBOT
versed bay
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aw man i got (1-sin2x)/cos2x

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its equivalent

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oh yeah it falls out

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after u simplify into tan and csc

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anyways cool

gilded orchid
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What

gilded orchid
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Pls dont do this

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Delete msg then ask what what

spice fjord
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I'm working it

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currently at cos^2x-sin^2x

gilded orchid
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Nice nice

spice fjord
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over (cosx+sinx)^2

gilded orchid
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Do you want aformula list

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I can send it for trigo

spice fjord
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I have one handy

gilded orchid
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Oh ok nice

spice fjord
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top part would simplify to cos2x

gilded orchid
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Yep

spice fjord
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bottom can be 1

gilded orchid
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No its not 1

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Its like sin²x+cos²x+2sinx cosx

spice fjord
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so FOIL bottom?

gilded orchid
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Sin²x+cos²x=1

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So we can write botton as

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1+2sin x cosx

spice fjord
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xI foiled and got $cos^2 x+2cosxsinx +sin^2x$

lunar rivet
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sin2x=2sinxcosx

wheat lionBOT
gilded orchid
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That is correct

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Then we just use identity

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Cos²x+sin²x=1

lunar rivet
gilded orchid
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Ok

spice fjord
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so 1 + 2cosxsinx

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1 + sin2x

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and we have our answer

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man trig identities is fun

gilded orchid
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Yeah

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They are until it becomes abstract

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Like you dont know where to aply which identity

spice fjord
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is that undergrad math?

lunar rivet
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all math is abstract it is only until we understand it that it becomes "fun"

spice fjord
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I've actually conditioned myself to enjoy the journey of learning it

gilded orchid
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Wonderful

spice fjord
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anyways, thanks everyone

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+close