Find the nature of triangle ?If, cos B = sin A / 2sin C.

Solution (By Examveda Team)

Method 1:

Given,

cos B = sin A / 2 sin C

Hence,

cos B * 2 sin C = sin A

Now,

sin (C + B) + sin (C-B) = sin (180 - (B +C))

sin (C + B) + sin (C-B) = sin (B +C)

sin (C +B) = 0

i.e. C = B
This is the case which says nature of the triangle is isosceles but if C=B then it must be that third angle also be equal so triangle may be equilateral as well.

Method 2:

2cosB *sinC = sin(180-(B+C)) = sin(B+C) = sinB cosC +cosB sinC

cosBsinC =sinBcosC
tanB = tanC

B = C