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Problem
Problem
If
α
\alpha
α
is a solution of the equation
3
sin
2
x
−
7
sin
x
+
2
=
0
3 \sin^2 x - 7 \sin x + 2 = 0
3
sin
2
x
−
7
sin
x
+
2
=
0
for
x
∈
[
0
,
2
π
]
x \in [0, 2\pi]
x
∈
[
0
,
2
π
]
, and
f
n
(
θ
)
=
sin
n
θ
+
cos
n
θ
f_n(\theta) = \sin^n \theta + \cos^n \theta
f
n
(
θ
)
=
sin
n
θ
+
cos
n
θ
, find the value of
f
4
(
α
)
f_4(\alpha)
f
4
(
α
)
. a.
97
81
\frac{97}{81}
81
97
b.
57
81
\frac{57}{81}
81
57
c.
65
81
\frac{65}{81}
81
65
d. 0
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