If in a triangle ABC, ∠C=60o, then 1a+c+1b+c= [IIT 1975]
A
1a+b+c
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
2a+b+c
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
3a+b+c
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
3a+b+c
cos C=π3⇒a2+b2−c2=ab ⇒b2+bc+a2+ac=ab+ac+bc+c2 ⇒ b(b+c)+a(a+c)=(a+c)(b+c)
Divide by (a+c)(b+c) and add 2 on both sides ⇒1+ba+c+1+ab+c=3⇒1a+c+1b+c=3a+b+c.