If √1+x^2 sin = x then prove that tan^2 + cot^2 = x^2 + 1/x^2
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Answer:
See Below
Explanation:
L
H
S
:
2
tan
(
x
2
)
1
+
tan
2
(
x
2
)
=
2
sin
(
x
2
)
cos
(
x
2
)
sec
2
(
x
2
)
-> use the property
1
+
tan
2
x
=
sec
2
x
=
2
sin
(
x
2
)
cos
(
x
2
)
1
cos
2
(
x
2
)
=
2
sin
(
x
2
)
cos
(
x
2
)
⋅
cos
2
(
x
2
)
1
=
2
sin
(
x
2
)
cos
(
x
2
)
⋅
cos
2
(
x
2
)
1
=
2
sin
(
x
2
)
cos
(
x
2
)
=
sin
2
(
x
2
)
->use the property
sin
2
x
=
2
sin
x
cos
x
=
sin
2
(
x
2
)
=
sin
x
=
R
H
S
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