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Answer:
We want to verify the identity
sin
(
a
)
1
+
cos
(
a
)
=
csc
(
a
)
−
cot
(
a
)
We will use
sin
2
(
a
)
+
cos
2
(
a
)
=
1
And the basic definitions of trigonometric functions
L
H
S
=
sin
(
a
)
1
+
cos
(
a
)
=
sin
(
a
)
(
1
−
cos
(
a
)
)
(
1
+
cos
(
a
)
)
(
1
−
cos
(
a
)
)
=
sin
(
a
)
−
sin
(
a
)
cos
(
a
)
1
−
cos
2
(
a
)
=
sin
(
a
)
−
sin
(
a
)
cos
(
a
)
sin
2
(
a
)
=
sin
(
a
)
sin
2
(
a
)
−
sin
(
a
)
cos
(
a
)
sin
2
(
a
)
=
1
sin
(
a
)
−
cos
(
a
)
sin
(
a
)
=
csc
(
a
)
−
cot
(
a
)
=
R
H
S
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