If sin (xy) + cos (xy) = 1 and tan (xy) is not equal to 1, then show that dy/dx - Maths - Differential Equations

Question

If sin (xy) + cos (xy) = 1 and tan (xy) is not equal to 1, then
show that dy/dx = -y/x

Varun.Rawat · Accepted Answer

We have,    sinxy + cosxy = 1⇒cos xy×ddxxy - sinxyddxxy = 0⇒ddxxycosxy - sinxy = 0⇒x × dydx + ycosxy - sinxy  = 0⇒x × dydx + y = 0    as, cosxy - sinxy ≠0⇒xdydx = -y⇒dydx = -yx

If sin (xy) + cos (xy) = 1 and tan (xy) is not equal to 1, then show that dy/dx = -y/x.