tan^2x - sin^2x = sec^2x.sin^2x
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Answer:
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Step-by-step explanation:
We need
tan
2
x
+
1
=
sec
2
x
(
a
+
b
)
(
a
−
b
)
=
a
2
−
b
2
Therefore,
L
H
S
=
tan
2
x
−
sin
2
x
=
(
tan
x
+
sin
x
)
(
tan
x
−
sin
x
)
=
(
sin
x
cos
x
+
sin
x
)
(
sin
x
cos
x
−
sin
x
)
=
sin
2
x
(
1
cos
x
+
1
)
(
1
cos
x
−
1
)
=
sin
2
x
(
sec
x
+
1
)
(
sec
x
−
1
)
=
sin
2
x
(
sec
2
x
−
1
)
=
sin
2
x
tan
2
x
=
R
H
S
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