BINOMIAL THEOREM

[tacit musk]

<@&1227988399579730072>

Note for OP

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[marsh lodge]

is it 12?

idt isme binomial ka kuch lagaya tho

i mean maybe my method is just too long

i just used trig identities

[brittle socket]

yep

how

[wintry stirrup]

Think about what kind of thingy combines both exponential and trigno stuff

There's one thing that comes to mind

e^{i(theta)}=cos(theta)+isin(theta)

[wintry stirrup]

So ${4 \choose r} sin(2rx) = {4 \choose r}Im(e^{2rx}) \text{which means what you want is basically} Im((1+e^{2x})^{4})$

[brazen wraith]

Lanceing the lot

[wintry stirrup]

U can simplify the stuff inside the bracket to get smth :P

[brittle socket]

ohh got itt

nice method

thanks

+solved @wintry stirrup

[marsh lodge]

this is kinda cool

[marsh lodge]

as a hint

try to play around with sinA+sinB

and using cos(2x) ka formula

uske baad virtually the same thing for the denominator

and you'll find that

it cancels out nicely

tho i like the method jo upar hai thats pretty cool ngl

[brittle socket]

that would be for denominator what abt numerator

sin(x)=cos(pi2-x)?

[marsh lodge]

mai toh numerator ki hi baat kar raha tha

💀

do you need me to send the full solution?

bhejdunga jab free hunga

[brittle socket]

yeah pls

[sonic fern]

How do you think of ts 💔