sin3theta=3sintheta - 4sintheta
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Answer:
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Step-by-step explanation:
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Answered by
0
Step-by-step explanation:
We have that
sin
(
3
θ
)
=
sin
(
2
θ
+
θ
)
=
sin
(
2
θ
)
⋅
cos
(
θ
)
+
cos
(
2
θ
)
⋅
sin
(
θ
)
=
2
sin
θ
⋅
cos
2
θ
+
sin
θ
⋅
(
1
−
2
sin
2
θ
)
=
2
⋅
sin
θ
⋅
(
1
−
sin
2
θ
)
+
sin
θ
⋅
(
1
−
2
sin
2
θ
)
=
3
⋅
sin
θ
−
4
sin
3
θ
We used the following trigonometric identities
sin
(
x
+
y
)
=
sin
x
⋅
cos
y
+
cos
x
⋅
sin
y
sin
(
2
x
)
=
2
sin
x
⋅
cos
x
cos
(
2
x
)
=
1
−
2
sin
2
x
cos
2
x
=
1
−
sin
2
x
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