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3
2023 Algebra/NT #3: Value of Trig Function
2023 Algebra/NT #3: Value of Trig Function
Source:
February 20, 2023
trigonometry
function
Problem Statement
Suppose
x
x
x
is a real number such that
sin
(
1
+
cos
2
x
+
sin
4
x
)
=
13
14
\sin(1 + \cos^2 x + \sin^4 x) = \tfrac{13}{14}
sin
(
1
+
cos
2
x
+
sin
4
x
)
=
14
13
. Compute
cos
(
1
+
sin
2
x
+
cos
4
x
)
\cos(1 + \sin^2 x + \cos^4 x)
cos
(
1
+
sin
2
x
+
cos
4
x
)
.
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