Prove that (1+cot2x)/sin2x= cosx
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(
csc
−
cot
x
)
2
=
1
−
cos
x
1
+
cos
x
(
csc
2
x
−
2
cot
x
csc
x
+
cot
2
x
)
=
1
−
cos
x
1
+
cos
x
(
1
sin
2
x
−
2
cos
x
sin
2
x
+
cos
2
x
sin
2
x
)
=
1
−
cos
x
1
+
cos
x
(
1
−
2
cos
x
+
cos
2
x
sin
2
x
)
=
1
−
cos
x
1
+
cos
x
(
(
1
−
cos
x
)
(
1
−
cos
x
)
1
−
cos
2
x
)
=
1
−
cos
x
1
+
cos
x
(
1
−
cos
x
(
1
−
cos
x
)
1
−
cos
x
(
1
+
cos
x
)
)
=
1
−
cos
x
1
+
cos
x
1
−
cos
x
1
+
cos
x
=
1
−
cos
x
1
+
cos
x
sauravh:
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