Question

Sin2x+2sin4x+sin6x=4cossquarexsin4x

Answer 1

Answer:
See the proof below
Explanation:
We need
sin
a
+
sin
b
=
2
sin
(
a
+
b
2
)
cos
(
a
−
b
2
)
cos
2
x
=
2
cos
2
x
−
1
Therefore,
L
H
S
=
sin
6
x
+
sin
2
x
+
2
sin
4
x
=
2
sin
(
6
x
+
2
x
2
)
cos
(
6
x
−
2
x
2
)
+
2
sin
4
x
=
2
sin
4
x
cos
2
x
+
2
sin
4
x
=
2
sin
4
x
(
cos
2
x
+
1
)
=
2
sin
4
x
(
2
cos
2
x
−
1
+
1
)
=
4
sin
4
x
cos
2
x
=
R
H
S
Q
E
D