Question

Prove the identity
sin(x-y)/cosxsiny=tanxcoty-1

Answer 1

Explanation:

`(sin(x - y))/(cos \: x \: sin \: y) \\ \\ = (sin \: x \: cos \: y -cos \: x \: sin \: y )/(cos \: x \: sin \: y) \\ \\ = (sin \: x \: cos \: y )/(cos \: x \: sin \: y) + (-cos \: x \: sin \: y )/(cos \: x \: sin \: y) \\ \\ = (sin \: x \:)/(cos \: x ) * (cos \: y )/(sin \: y) - 1 \\ \\ = tan \: x \: cot \: y - 1 \\ \\ \therefore \: (sin(x - y))/(cos \: x \: sin \: y) = tan \: x \: cot \: y - 1 \\ \\ thus \: proved \\`