if tan(a+b-c)/tan(a-b+c)=tan(c)/tan(b) find sin(b-c)

We know that a+b+c=p

So tan (a+b-c)/tan(a-b+c) =tanc/tanb

Tan(p-2c)/tan(p-2b) =tanc/tanb

tan 2c/tan 2b =tanc/tanb

{2tanc/(1-tan²c)}/{2tanb/(1-tan²b)} =tanc/tanb

(1-tan²b)/(1-tan²c) =1

Tan²b=tan²c

Tanb=tanc

Tanb=tanc or tan(p+c)

b=c or p+c

b-c=0 or p

so sin(b-c) = sin0 or p

sin(b-c) =0 or p

Hence Ans is 0 orp

Thanks & Regards

Rinkoo Gupta

AskIITians Faculty