सिद्ध कीजिए कि -
` (sin (A-B))/(sin A sinB) + (sin(B-C))/(sin B sin C)+ (sin (C-A))/(sin Csin A)=0`

Explanation

` (sin(A-B))/(sinAsinB) = ( sinA cos B - cos A sinB)/(sinA sinB)`
` = (sin A cosB)/(sinA sinB) - (cos A sinB)/(sinA sinB)`
इसी प्रकार सिद्ध कर सकते है कि
` (sin (B-C))/(sinB sinC)= cot C - cot B`
` (sin (C-A))/(sinC sinA) = cot A - cot C`
` :. L.H.S = (sin(A-B))/(sinAsinB)+ (sin(B-C))/(sin B sin C) + (sin (C - A))/(sin C sinA)`
` = cot B - cot A + cot C - cot B + cot A - cot C`
` = 0 = R.H.S`