sin 10 theta + sin 2 theta =
Answers
Answered by
1
Answer:
You can solve it with the formula sum-to-product, that says:
sin
α
+
sin
β
=
2
sin
(
α
+
β
2
)
cos
(
α
−
β
2
)
,
so:
sin
2
θ
+
sin
4
θ
=
0
⇒
2
sin
(
2
θ
+
4
θ
2
)
cos
(
2
θ
−
4
θ
2
)
=
0
⇒
sin
3
θ
cos
(
−
θ
)
=
0
so:
sin
3
θ
=
0
⇒
3
θ
=
k
π
⇒
θ
=
k
π
3
and:
cos
(
−
θ
)
=
0
⇒
cos
θ
=
0
⇒
θ
=
π
2
+
k
π
.
(remembering that
cos
(
−
α
)
=
cos
α
).
There is another way:
sin
2
θ
=
−
sin
4
θ
⇒
sin
3
θ
=
sin
(
−
4
θ
)
(remembering that
sin
(
−
α
)
=
−
sin
α
),
and than remembering that two sini are equal when the angles are equal or if the angles are supplementary,
2
θ
=
−
4
θ
+
2
k
π
⇒
6
θ
=
2
k
π
⇒
θ
=
k
π
3
and
2
θ
=
π
−
(
−
4
θ
)
+
2
k
π
⇒
2
θ
=
π
+
4
θ
+
2
k
π
⇒
−
2
θ
=
π
+
2
k
π
⇒
θ
=
−
π
2
−
k
π
that is formally identical to the second solution found before.
Answered by
0
Answer:
ans
1
one....
sin 10 and theta
can.cle equal s to
one 1...
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