1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# Assertion (A) : The maximum value of f(x)=sin−1x+cos−1x+tan−1x is 3π4Reason (R) : sin−1x>cos−1x for all x in R

A
Both A and R are true and R is the correct explanation of A
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
Both A and R are true and R is not correct explanation of A
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
A is true but R is false
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
A is false but R is true
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is D A is true but R is falsef(x)=sin−1(x)+cos−1(x)+tan−1(x)Now sin−1(x)+cos−1(x)=π2Hencef(x)=tan−1(x)+π2Substituting x=1, we get the maximum as π4+π2=3π4Reason.The intersection point of sin(x) and cos(x) is x=π4 between [0,π2].Now cos(x) is a decreasing function in the above interval while sin(x) is an increasing function in the above interval.Also.cos(x)>sin(x) between [0,π4] while sin(x)>cos(x) between [π4,π2]Hencesin−1(x)>cos−1(x) between [1√2,1].Hence reason is false.

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Property 5
MATHEMATICS
Watch in App
Join BYJU'S Learning Program