Question

verify that is an indentity

b) Sin(x-y)=(1-cotx tany)/(csc x sec y)

Answer 1

sin(x-y)=(1-cot(x)*tan(y))/(csc(x)*sec(y))


sin(x-y)=(1-(cos(x))/(sin(x))*(sin(y))/(cos(y)))/(1/sin(x)*1/cos(y))


sin(x-y)=(1-(cos(x)*sin(y))/(sin(x)*cos(y)))/(1/(sin(x)*cos(y)))


Now multiply EVERY term on the right side by the inner LCD sin(x)*cos(y) to clear out the inner fractions and simplify


sin(x-y)=(sin(x)*cos(y)-cos(x)*sin(y))/(1)


sin(x-y)=sin(x)*cos(y)-cos(x)*sin(y)


sin(x-y)=sin(x-y)