if y=sinx+cosx /sinx-cosx then find dy/dx
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Answer:
Given
sin
x
+
sin
2
x
=
1
⇒
sin
x
=
1
−
sin
2
x
⇒
sin
x
=
cos
2
x
⇒
sin
2
x
=
cos
4
x
⇒
1
−
cos
2
x
=
cos
4
x
⇒
cos
2
x
+
cos
4
x
=
1
...
...
[
1
]
Again
sin
x
+
sin
2
x
=
1
⇒
sin
x
sin
2
x
+
sin
2
x
sin
2
x
=
1
sin
2
x
⇒
csc
x
+
1
=
csc
2
x
⇒
csc
x
=
csc
2
x
−
1
⇒
csc
x
=
cot
2
x
⇒
csc
2
x
=
cot
4
x
⇒
1
+
cot
2
x
=
cot
4
x
⇒
cot
4
x
−
cot
2
x
=
1
...
...
.
.
[
2
]
Adding [1] and [2]
we get
cos
2
x
+
cos
4
x
+
cot
4
x
−
cot
2
x
=
1
+
1
=
2
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