Trig identity

[jolly sparrow]

Pretty sure i got this wrong because it seems too simple. My professor has been out for two weeks so i’m pretty lost.

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[whole edge]

What is sin(2x) in terms of cos(x) and sin(x)?

[jolly sparrow]

2sin(x)cos(x) right?

[whole edge]

Yes

So you can factor

[agile stone]

[
\frac{\sin 2 \theta - \cos \theta}{2 \sin \theta - 1} \neq
\frac{\sin 2 \theta - \cos \theta}{\sin 2 \theta - 1} \neq
\frac{\sin 2 \theta}{\sin 2 \theta} \cdot \frac{- \cos \theta}{- 1}
]

[strong loom]

Invariance

[agile stone]

all of those are different

[strong loom]

Invariance

[jolly sparrow]

okay thank you. i will try again after i finish eating lunch

[whole edge]

Oh is that what’s written I was a bit confused 😅

[whole edge]

Ight have a nice meal

[jolly sparrow]

hey i just retried it, just wanted to know if this looks right to you

[jolly sparrow]

hey i just retried it, just wanted to know if this looks right to you

sorry if it’s wrong yall i swear im trying😭

[dim marlin]

you need to take cos(x) common

[jolly sparrow]

cos(x) common? i’m sorry i don’t understand

[dim marlin]

like so

[whole edge]

2cos(x)sin(x)-cos(x)=cos(x)(2sin(x)-1)

[dim marlin]

for example say, (a-1)b + b

this can be written as b{ (a-1) +1 }

could you tell me what would this equation look like when you take y common?

[jolly sparrow]

i know i’m supposed to factor but i have to remember how, give me a minute

never mind i have no idea. it’s okay if it’s too much too explain.

[dim marlin]

no its completely fine

how about this?

[jolly sparrow]

x(a+1) ?

[dim marlin]

ah good

[dim marlin]

now try this

you could also substitute (ax+4) with "t" if that makes you feel more comfortable

[jolly sparrow]

so would it y((ax+4)+k))

[dim marlin]

yeah good job :)

[dim marlin]

now can you see a " (x)y + y " here?

[jolly sparrow]

yea is would be the cosines. but if i tried it, it would come out different than the one you sent

give me a second let me see

[dim marlin]

id like to uh point that the operations you used here is wrong

[jolly sparrow]

what do you mean?

[dim marlin]

this is not correct

[jolly sparrow]

oh okay, i’m really bad with fractions. i’m guessing the a numerator cancels but the denominator a stays for x-x/a?

[dim marlin]

no see ax-x is really just (a-1)x

[jolly sparrow]

okay that makes sense

[dim marlin]

so you can not cut a from both the numerator and the denominator

[jolly sparrow]

even after i’ve simplified it this far? or is that just referring to my original attempt?

[dim marlin]

yeah i was referring to the original one

[dim marlin]

here you can see (2sinx - 1) in the numerator and in the denominator

so you can cancel them out to get your answer :)

[jolly sparrow]

amazing🙏🏻

you are a truly great teacher even through text messages lol

thanks

[dim marlin]

np

[jolly sparrow]

+close