Sinxcosy(cotxtany-1)
To simplify the expression sin(x)cos(y)(cot(x)tan(y)-1), we can apply trigonometric identities and simplification techniques step by step:
Step 1: Identify the reciprocal identities:
- cot(x) is the reciprocal of tan(x), so cot(x) = 1/tan(x)
- tan(y) is the reciprocal of cot(y), so tan(y) = 1/cot(y)
Step 2: Substitute the reciprocal identities back into the expression:
sin(x)cos(y)(1/tan(x) * 1/cot(y) - 1)
Step 3: Simplify the expression:
Multiplying the denominators, we get:
sin(x)cos(y)((1*1)/(tan(x)*cot(y)) - 1)
Step 4: Simplify further using the identity tan(x) * cot(y) = 1:
sin(x)cos(y)(1 - 1) = sin(x)cos(y)(0) = 0
Therefore, the simplified expression is 0.