Solution We differentiate the relationship directly with respect to x, i e ,
(sin )
dy
d
y
dx
+dx
 =
d(cos )
x
dx
which implies using chain rule
cos
dy
ydy
dx
dx
+
⋅
 = – sin x
This gives
dy
dx  =
sin
1
cos
x
y
− +
where
y ≠ (2n + 1) π
Rationalised 2023-24
 MATHEMATICS
124
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