Question

Solve:

cos x cos y dy + sin x sin y dx= 0

The answer give in the book is : sin y = C cos x

Answer 1

hii frnd plz find the attachment here ur answer

hope its helpful

Answer 2

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
By taking integration both side,
⇒ ∫cos(y)/sin(y) dy = -∫sin(x).cos(x).dx
⇒ ∫cot(y) dy = -∫tan(x).dx
⇒ ln|siny| = - (-ln|cos(x)| +c)
⇒ ln|sin(y)| = ln|cos(x)| + ln|C|     
⇒ ln|sin(y)| = ln|C.cos(x)|                ∵ ln(a) +ln(b) = ln(ab)
⇒ sin(y) = C.cos(x)