62 Replies
@Apu
Note for OP
+solved @user1 @user2... to close the thread when your doubt is solved. Mention the users who helped you solve the doubt. This will be added to their stats.i dont have a doubt in the working of the solution
i just wanna know what are the hints for such particular substitution ( example 3 and 4)
like what info does the question contain to make my brain think of 2x+2= 3tantheta
You're asking for 3 ohh
I was typing for 4
both
See for 3 I have a good explanation
Root k niche perfect square banaya kro sbse phele waha se kuch hint mil jata hai
You see a square term forming
wahan tak aa gya tha
Usme when you see a^2+x^2
To vahan pe you definitely know ki somehow tan or sec involved hoga
'cause sec^2 = 1 + tan^2
why not cot or cosec
Vo kar lo
Usse bhi same result aayega
Not much of a difference
Whenever you see squares being added inside a square root
First thought should be trigonometric substitution
Chahe numerator me ho chahe denominator me
This works is virtually 90% of the cases
And 4 me
You got this one to 4 ka bolun?
@hardcoreisdead
Yaar gayab na hua karo
ek min processing
Okay sorry lol 😭
i am convincing myself for this
Hmm hmm
yeah makes sense now
Try visualising this in different contexts
Alag alag situation me
Almost everywhere
It will make sense
So 4 now?
Bataun?
yep
Yeah so usme to andar ka expression hai log ke
You remember from trigonometry how that relates to Cos2x
I hope you do remember the relation exactly 'cause I frankly don't
I just remember it looked something like that
cos2x= 2cos^2x-1= 1-2sin^2x
And agar ln(something) hai
Try converting this to just sin and cos
Log ke andar jo hai vaise hi kuch milega
Thodi trigo hai heavy
I gotta pick my pen and paper too I guess lol
Trig after a long time:)
cos^2x-sin^2x
Somehow take it to a single power
a^2 - b^2
Identity lagayo
matlab?
Difference of squares yaar
we can see that (sinx+cosx)(sinx-cosx)= co2x
ill try subbing in this
(Cosx-sinx) buddy
Not sinx - cosx
yeah
$ \ln \frac {\Bigg \bigg{2 \times \sin{x} \cos{x} \bigg} {\cos{2x}} $
Chala kyun nahi 😭
Itni mehnat se likha tha
oh my my latex wale bhaiya 🥵
Aaj hi seekhna shuru kiya tha maths isme yaar 😭
bruh just use desmos and snipping tool
Socha test kar lun
works like a charm
Are I was just trying to practice
yeah yeah.
If I remember or not
What I studied in the morning 😭
Ahhmm so isme upar sin2x laga do
1 + sin2x
Divided by cos2x
GOD DAMN
BHAI KI MATHS STRONG HAI
Naah bhai 😭🙏
Iske aage tan2x ban jayega
If I remember correctly
Then that can be converted into sinx and cosx
In that form only
Jo ln ke andar di hui hai
I don't remember how
But somehow ho jaana chahiye
ln(sec2x+tan2x)
easy derivative
Huh?
Ye kahan bana?
1+sin2x)/cos2x
Accha haan
Ohh shit
Sorry
Ban gaya I guess
koi na
That tan2x can be converted though
The expression given in the module holds a lot of importance I can tell you by the look of it
so the crux of this post is tan substitution and simplifying the most complex term first
@SirLancelotDuLac must spawn now
Yeah that
But that expression is very important
yeahh
Jisko directly change Kiya hai
dude integration is so random
requires raw iq
And yet it's not
.:)
EXACTLY
Imma look at it tomorrow 😭
soln dekh ke lagta hai " who tfs gonna think that" and when i actually look at it carefully
its just
pure logic
You saw my post on media last night?
That's very insightful
Give it a look
Integration pe hi hai ek chiz pe
tag or forward
Tagging wait
Just one expression please 😭🙏
I'm very curious too now
'cause I vaguely remember it
Okay, actually I think the way to go would be write the everything inside ln as tan(x+pi/4) first. Then the derivative of ln(tan(x+pi/4)) gives 1/cos(2x) ig?
Yeah the crux remains solving the ln() term first
+solved @Enamine @SirLancelotDuLac
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