ITF
Bhai isme koi meri last step ek bar bata do shi hai kya jisme cos^-1 ki inequality solve kri hai
7 Replies
@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.also do tell me about the graph ig its wrong
Y= cos-¹(2x²-1)
= Cos -¹[cos (2 cos-¹ (x) ) ]
Say 2 cos-¹(x)= t
So we have to first make the graph of cos -¹ ( cos(t) )
Ab according to values of t you'll get your value of y [ straight line mei (x,y) mei se x toh mil gaya y mil jaega straight line ka equation likhne ke liye graphically slope bhi mil jaegi aur ek point bhi.
2 cos-¹(x) belongs to (0,π)
So we'll have 2 cos-¹x as it is
2 cos -¹(x) belongs to (π,2π)
We have the graph
Y-π = -(t-π)
Y+t =2π
Y= 2π- t
So y = 2π- 2 cos-¹(x)
And so on
So
2 cos-¹(x) belongs to (0,π)
Means
Cos-¹(x) belongs to (0,π/2)
Or X≥0
Lly,
2 cos-¹(x) belongs to (π,2π) means ,
Cos-¹(x) belongs to (π/2,π)
Which means x ≤0
Oh please note all the brackets I have used so far are the closed ones
Obv cos-¹(anything) can only Belong to [0,π]
So we'll have to note only in those ranges
Thanks brother
+solved @Sam crazy effort man
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