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

# In an acute angles triangle ABC if cosA,1−cosB,cosC are in A.P. and sinA+sinC=1, then ∠B is equal to

A
π4
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
π3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
π6
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
None of these
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is C π6Given sinA+sinC=1cosA+cosC=2(1−cosB)we know that A+B+C=π⇒2cos(A+C2)cos(A−C2)=4sin2B2⇒2cos(π−B2)cos(A−C2)−4sin2B2=0⇒sinB2[cos(A−C2)−2sin(π−(A+C)2)]=0 since 2cosccosd=cos(c+d)−cos(c−d)⇒sinB2[cos(A−C2)−2cos(A+C2)]=0as sinB2≠0 so cos(A−C2)=2cos(A+C2)⇒cos(A−C2)=2sinB2multiplying both sides by 2cosB2, we get2cosB2cos(A−C2)=sinB⇒2sin(A+C2)cos(A−C2)=2sinB⇒sinA+sinC=2sinB since 2sinccosd=sin(c+d)+sin(c−d)⇒sinB=12⇒∠B=π6

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program