sin 3 theta = sin theta (2 cos 2 theta + 1
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Answer:
21-Jun-2018 · 1 answer
Please see the proof below. Explanation: We need. sin2θ=2sinθcosθ. cos2θ+sin2θ=1. cos2θ =1−2sin2θ. First calculate sin3θ. sin3θ=sin(2θ+θ). =sin2θcosθ+cos2θsinθ. =2sinθcos2θ+(1−2sin2θ)sinθ.
Please see the proof below Explanation: We need sin2θ=2sinθcosθ cos2θ+sin2θ=1 cos2θ=1−2sin2θ First calculate sin3θ sin3θ=sin(2θ+θ) ... More
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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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