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

If in a triangle ABC,2cosAa+cosBb+2cosCc=abc+bac.FindA.

A
π2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
π4
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
π6
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
π3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A π2
2cosAa+2cosBb+2cosCc=abc+bac
using cosA=b2+c2a22bc,.... (cosine rule)
2a(b2+c2a22bc)+1b(c2+a2b22ca)+2c(a2+b2c22ab)=abc+bac
2(b2+c2a2)2abc+c2+a2b22abc+2(a2+b2c2)2abc=abc+bac
Taking LCM
2(b2+c2a2)+c2+a2b2+2(a2+b2c2)2abc=a2+b2abc
2b2+2c22a2+c2+a2b2+2a2+2b22c2=2a2+2b2
2a2+c2+a2b2+2b2=0a2+c2+b2=0b2+c2=a2
Above expression is pythagoras theorem
a is hypotenuse of triangle ABC
opposite angle is 90o
A=90o=π2

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Cosine Rule
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon