Let f(x)=⎧⎨⎩−2sinx,x≤−mAsinx+B,−m<x<mcosx,x≥m be a continuous function, where m is the principal solution of the equation sin3x+sinxcosx+cos3x=1. If m>0, then
A
A=−1,B=1
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
m=π
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
m=π2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
A=1,B=−1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct options are AA=−1,B=1 Cm=π2 sin3x+sinxcosx+cos3x=1 ⇒(sin3x+cos3x)−(1−sinxcosx)=0 ⇒(sinx+cosx)(1−sinxcosx)−(1−sinxcosx)=0 ⇒(1−sinxcosx)(sinx+cosx−1)=0⇒sinxcosx=1 or sinx+cosx=1⇒sin2x=2 or sinx+cosx=1 sin2x=2 is not possible.
sinx+cosx=1 ⇒sinxsinπ4+cosxcosπ4=1√2 ⇒cos(x−π4)=cosπ4 ⇒x=0,π2,2π But m is a principal solution with m>0. So, m=π2