ITF
The complete set of values of x for which 2 tan − 1 (x) + cos − 1 ( 1 − x2/ 1 + x2 ) is independent of x is :
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@Apu
Note for OP
+solved @user to close the thread when your doubt is solved. Mention the user who helped you solve the doubt. This will be added to their stats.it is tan inverse x and cos inverse
its literally screaming to take x = tan theta
leliya
uske aage kya krna h
4tan-1x bnaliya
now what to do
send me ques pic
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from what I understand independent of x. I dont think theres any value coz y = 4tan-1x will never be independent of x. tan(y4) = x will always be dependent upon x so I guess x (- phi
how the fuck are you on discord?
bhai pc pe bhi to chalta hai discord
what will be the range of x then??
phi means nothing. Expression is never independent of x
answer is -infinity to zero
independent of x? or dependent of x?
independent
cos^-1 (1-x^2/1+x^2) = 2tan^-1(x) when tan^-1x is between 0 and pi/2, hence it applies when x is positive
Since tan^-1x is an odd function but the other is even, cos^-1(1-x^2/1+x^2) = -2tan^-1x when x is nonpositive
so the expression becomes 0 when x is negative
so yeah the answer is (-inf, 0]
tanks
its always the fucking domain in ITF....
+solved @Comrade Rock Astley
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