If A+B+C=180 and sin a= sin b sin c prove that

Question

cot a= 1- cot b cot c

Answer 1

Solution:

Using the identity sin(A+B) = sin A cos B + cos A sin B, we can rewrite the equation as follows:

sin A + sin B sin C = cos B cos C

Using the identity cot A = 1/tan A, we can rewrite the equation as follows:

cot A = 1/sin A + 1/sin B sin C

Substituting 1-cot B cot C for 1/sin B sin C, we get:

cot A = 1 - cot B cot C