prove that: 1-tan²A+tan⁴A=cos²A(1+tan⁶A)
Answers
Answered by
1
Step-by-step explanation:
We know that
sec
2
A
=
tan
2
A
+
1
Hence
sec
6
A
=
(
sec
2
A
)
3
=
(
tan
2
A
+
1
)
3
Now
(
a
+
b
)
3
=
a
3
+
3
a
2
b
+
3
a
b
2
+
b
3
, which can alsobe written as
=
a
3
+
3
a
b
(
a
+
b
)
+
b
3
Considering
a
=
tan
2
A
and
b
=
1
we have
(
tan
2
A
+
1
)
3
=
(
tan
2
A
)
3
+
3
×
tan
2
A
×
1
(
tan
2
A
+
1
)
+
1
3
=
tan
6
A
+
3
tan
2
A
sec
2
A
+
1
Here we have converted
tan
2
A
+
1
back to
sec
2
A
.
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