Question

cosx.cosy dy-sinx.siny dx=0

Answer 1

Answer:

Step-by-step explanation:

cos x. cos y dy - sin x. sin y dx=0

cos x. cos y dy = sin x. sin y dx

(cos y/sin y) dy = (sin x/cos x) dx

cot y. dy = tan x. dx

Now integrate both sides :

(integral) cot y. dy = ln|sin y| + ln c₁ ....(1)

(integral) tan x. dx = - ln|cos x| + ln c₂ ....(2)

(1) & (2),

ln|sin y| + ln c₁ = -ln|cos x| + ln c₂

ln|sin y| + ln |cos x| = ln c₂ - ln c₁

ln|cos x. sin y| = ln (c₂/c₁)

cos x. sin y = c₂/c₁ = c₃

cos x. sin y = c₃