1 answer:
Answer:csc
2
(
x
)
=
1
sin
2
(
x
)
Step-by-step explanation:
d
d
x
[
csc
2
(
x
)
]
=
−
2
cot
x
csc
2
x
Explanation:
csc
2
(
x
)
=
1
sin
2
(
x
)
d
d
x
[
csc
2
(
x
)
]
=
d
d
x
[
1
sin
2
(
x
)
]
d
d
x
[
1
sin
2
(
x
)
]
=
d
d
x
[
[
sin
(
x
)
]
−
2
]
let
u
=
sin
x
d
d
x
[
[
sin
(
x
)
]
−
2
]
=
d
d
u
[
u
−
2
]
d
d
x
[
sin
x
]
d
d
u
[
u
−
2
]
=
−
2
u
−
3
d
d
x
[
sin
x
]
=
cos
x
d
d
x
[
[
sin
(
x
)
]
−
2
]
=
−
2
u
−
3
cos
x
=
−
2
cos
x
sin
3
x
cos
x
sin
x
=
cot
x
⇒
−
2
cos
x
sin
3
x
=
−
2
cot
x
sin
2
x
1
sin
2
x
=
csc
2
x
⇒
−
2
cot
x
csc
2
x
d
d
x
[
csc
2
(
x
)
]
=
−
2
cot
x
csc
2
x
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