If A+B+C=180 and sin a= sin b sin c prove that
cot a= 1- cot b cot c
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