wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Let y=(cot1x)(cot1(x)) and range of y(0,aπ2b], then the value of a+b is

A
2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
4
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
5
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
6
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C 5
Given : y=(cot1x)(cot1(x))
y=cot1x[πcot1(x)]
As cot1(x)>0, (πcot1(x))>0

Using A.M. G.M., we get
cot1x+(πcot1(x))2(cot1x)[πcot1(x)]0<cot1(x)(πcot1(x))π20<yπ24a=1, b=4a+b=5

Alternate solution
y=(cot1x)(cot1(x))
y=(cot1x)(πcot1(x))
Let t=cot1x
y=t2+πt
t(0,π)

f(0)=0
f(π)=0
and
D4a=π204=π24
Hence, y(0,π24]
a=1,b=4
a+b=1+4=5

flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon