sin 3 theta ( 1 - cos 2 theta ) equals to
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Step-by-step explanation:
We need
sin
2
θ
=
2
sin
θ
cos
θ
cos
2
θ
+
sin
2
θ
=
1
cos
2
θ
=
1
−
2
sin
2
θ
First calculate
sin
3
θ
sin
3
θ
=
sin
(
2
θ
+
θ
)
=
sin
2
θ
cos
θ
+
cos
2
θ
sin
θ
=
2
sin
θ
cos
2
θ
+
(
1
−
2
sin
2
θ
)
sin
θ
=
2
sin
θ
(
1
−
sin
2
θ
)
+
(
1
−
2
sin
2
θ
)
sin
θ
=
3
sin
θ
−
4
sin
3
θ
And
1
+
2
cos
2
θ
=
1
+
2
(
1
−
2
sin
2
θ
)
=
3
−
4
sin
2
θ
Therefore,
R
H
S
=
sin
3
θ
1
+
2
cos
2
θ
=
3
sin
θ
−
4
sin
3
θ
3
−
4
sin
2
θ
=
sin
θ
3
−
4
sin
2
θ
3
−
4
sin
2
θ
=
sin
θ
=
R
H
S
Q
E
D
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