ITF simplification
Express $\tan^{-1}\left(\frac{\cos x}{1-\sin x}\right),\ \ -\frac{3\pi}{2}<x<\frac{\pi}{2}$ in the simplest form.
58 Replies
Nimboi
@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.expressing sin(x) and cos(x) in their tan(x/2) forms, I got here:
$\tan^{-1}\left(\frac{1}{1-\tan^{2}\left(\frac{x}{2}\right)}\right)$
Nimboi
what now?
hmmm
gimme a sec
cos(θ)/1-sin(θ) can be expresssed as tan(π/4+θ/2)
you're correct
bro what is that domain given
they used a different method to do that
send
camera doesnt work ill just tell you
I just have in my notes as standard result
alr
cosx = sin(pi/2 - x)
1 - sinx = 1 - cos(pi/2 - x)
sin(pi/2 - x) = 2sin(pi/4 - x /2)cos(pi/4 - x/2)
oh so just derivation of it
alr got it
1 - cos(pi/2 - x) = 2sin^2(pi/4 - x/2)
yeah alr nice
u got it right?
yeah but can i proceed from here
cuz i thought of that first
hmmm
didnt think to express cos(x) as sin(pi/2 - x) and whatnot
yeah me neither
keep in mind tho
bet
anyways for boards cant use that standard result as a standard result
true
@BlindSniper (BS) made a typo
its 1 - tan(x/2) in the denom
$\tan^{-1}\left(\frac{1}{1-\tan\left(\frac{x}{2}\right)}\right)$
Nimboi
oh makes sense
I wasn't getting what you got
ok lemme see
@BlindSniper (BS) made a mistake along the way just start from the original problem lol
main thoda stupid
wow
r u state board or cbse
cbse lmao
havent done good math in a while
then thoda problem to zaroor hai
state board u can directly write
hmmmmmm
Yo what's going on?
ignore the silly in the middle
look at the problem on top
i wanna do it by expressing sin and cos as their tan(x/2) identities
if that'll somehow work
tried to reverse it but getting nowhere
Hmmm
i got it
nice
tan(x/2) in terms of sinx and cosx
but you would need to know the answer for this
yeah you get here and then
lite le baap
1 = tan(pi/4)
yeah sure but
.
yeah the answer is pi/4 + x/2
ah ok you mean
I'm saying
would you have known the answer if you didn't see the solution?
hard to think of that without knowing its of that form?
yeah
if i knew i had to remove the tan then maybe yes
this is a neat trick
it seems more thinkable to me than expressing cosx as sin(pi/2 - x)
yea true ig
but it kind of reminds me of the complex number questions
which ones?
whhere you have to convert in terms of cistheta
lemme get one rq
here you take it as sin(pi/2-x)
pretty fire
man what the
how does one have that level of foresight
or is it more just screwing around
nah but this is easy in this case but if you get directly in a trigonometry question I wouldn't think of it
💀
if you see it that way
well, thanks dude
ill mark as solved
👍
+solved @BlindSniper (BS)
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