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Mathematics
Mathematics
Problem
If the quadratic equation
4
sec
2
α
x
2
+
2
x
+
(
β
2
−
β
+
1
2
)
=
0
4^{\sec^2 \alpha} x^2 + 2x + \left( \beta^2 - \beta + \frac{1}{2} \right) = 0
4
s
e
c
2
α
x
2
+
2
x
+
(
β
2
−
β
+
2
1
)
=
0
has real roots, then find all the possible values of
cos
α
+
cos
−
1
β
\cos \alpha + \cos^{-1} \beta
cos
α
+
cos
−
1
β
.
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