tan^2x= 3(secx-1)
prove that
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Answer:
To prove
tan
2
(
x
)
sec
(
x
)
−
1
=
sec
(
x
)
+
1
Use the identity
1
+
tan
2
(
x
)
=
sec
2
(
x
)
We can rewrite this as
tan
2
(
x
)
=
sec
2
(
x
)
−
1
Now back to our problem
LHS
=
tan
2
(
x
)
sec
(
x
)
−
1
=
sec
2
(
x
)
−
1
sec
(
x
)
−
1
Recall the difference of square rule
a
2
−
b
2
=
(
a
−
b
)
(
a
+
b
)
We need to apply that for
sec
2
(
x
)
−
1
=
(
sec
(
x
)
−
1
)
(
sec
(
x
)
+
1
)
sec
(
x
)
−
1
=
sec
(
x
)
−
1
(
sec
(
x
)
+
1
)
sec
(
x
)
−
1
=
sec
(
x
)
+
1
=
RHS
Therefore, LHS = RHS thus proved.
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