1
Prove that: cos^6 + sin^6 = (5 + 3* cos4theta)
Answers
Answered by
0
Answer:
teacher se puch. bcccccc
Answered by
1
Step-by-step explanation:
We'll use
→
a
3
+
b
3
=
(
a
+
b
)
(
a
2
−
a
b
+
b
2
)
→
a
2
+
b
2
=
(
a
−
b
)
2
+
2
a
b
→
sin
2
x
+
cos
2
x
=
1
→
2
cos
2
x
=
1
+
cos
2
x
and
→
2
sin
2
x
=
1
−
cos
2
x
L
H
S
=
cos
6
(
x
)
+
sin
6
(
x
)
=
(
cos
2
x
)
3
+
(
sin
2
x
)
3
=
[
cos
2
x
+
sin
2
x
]
[
(
cos
2
x
)
2
−
cos
2
x
⋅
sin
2
x
+
sin
2
x
)
2
]
=
1
⋅
[
(
cos
2
x
−
sin
2
x
)
2
+
2
cos
2
x
⋅
sin
2
x
−
cos
2
x
⋅
sin
2
x
]
=
[
cos
2
(
2
x
)
+
cos
2
x
⋅
sin
2
x
]
=
1
4
[
4
cos
2
(
2
x
)
+
4
cos
2
x
⋅
sin
2
x
]
=
1
4
[
2
(
1
+
cos
4
x
)
+
sin
2
(
2
x
)
]
=
2
4
⋅
2
[
2
+
2
cos
4
x
+
sin
2
(
2
x
)
]
=
1
8
[
4
+
4
cos
4
x
+
2
sin
2
(
2
x
)
]
=
1
8
[
4
+
4
cos
4
x
+
1
−
cos
4
x
]
=
1
8
[
5
+
3
cos
4
x
]
=
R
H
S
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