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Mathematics
Mathematics
Problem
If
tan
θ
i
\tan \theta_i
tan
θ
i
,
i
=
1
,
2
,
3
,
4
i = 1, 2, 3, 4
i
=
1
,
2
,
3
,
4
are the roots of equation
x
4
−
x
3
sin
2
β
+
x
2
cos
2
β
−
x
cos
β
−
sin
β
=
0
x^4 - x^3 \sin 2\beta + x^2 \cos 2\beta - x \cos \beta - \sin \beta = 0
x
4
−
x
3
sin
2
β
+
x
2
cos
2
β
−
x
cos
β
−
sin
β
=
0
, then
tan
(
θ
1
+
θ
2
+
θ
3
+
θ
4
)
=
\tan(\theta_1 + \theta_2 + \theta_3 + \theta_4) =
tan
(
θ
1
+
θ
2
+
θ
3
+
θ
4
)
=
(a)
sin
β
\sin \beta
sin
β
(b)
cos
β
\cos \beta
cos
β
(c)
tan
β
\tan \beta
tan
β
(d)
cot
β
\cot \beta
cot
β
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