2 cos x+ cos 3x = 0
Answers
Answered by
1
Answer:
Note that
cos
3
x
can be rewritten as
cos
(
2
x
+
x
)
.
cos
x
+
cos
(
2
x
+
x
)
=
0
Now use
cos
(
A
+
B
)
=
cos
A
cos
B
−
sin
A
sin
B
.
cos
x
+
cos
2
x
cos
x
−
sin
2
x
sin
x
=
0
Apply
cos
2
x
=
2
cos
2
x
−
1
and
sin
2
x
=
2
sin
x
cos
x
.
cos
x
+
(
2
cos
2
x
−
1
)
cos
x
−
2
sin
x
cos
x
(
sin
x
)
=
0
cos
x
+
2
cos
3
x
−
cos
x
−
2
sin
2
x
cos
x
=
0
Use
sin
2
x
+
cos
2
x
=
1
:
cos
x
+
2
cos
3
x
−
cos
x
−
2
(
1
−
cos
2
x
)
cos
x
=
0
cos
x
+
2
cos
3
x
−
cos
x
−
2
cos
x
+
2
cos
3
x
=
0
4
cos
3
x
−
2
cos
x
=
0
Factor:
2
cos
x
(
2
cos
2
x
−
1
)
=
0
We have
cos
x
=
0
x
=
π
2
,
3
π
2
AND
cos
x
=
±
1
√
2
x
=
π
4
,
3
π
4
,
5
π
4
and
7
π
4
Answered by
0
Answer:
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