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Problems
Mathematics
Mathematics
Problem
For any
θ
∈
(
π
4
,
π
2
)
\theta \in \left(\frac{\pi}{4}, \frac{\pi}{2}\right)
θ
∈
(
4
π
,
2
π
)
, the expression
3
(
sin
θ
−
cos
θ
)
4
+
6
(
sin
θ
+
cos
θ
)
2
+
4
sin
6
θ
3(\sin\theta - \cos\theta)^4 + 6(\sin\theta + \cos\theta)^2 + 4\sin^6\theta
3
(
sin
θ
−
cos
θ
)
4
+
6
(
sin
θ
+
cos
θ
)
2
+
4
sin
6
θ
equals : (1)
13
−
4
cos
6
θ
13 - 4 \cos^6\theta
13
−
4
cos
6
θ
(2)
13
−
4
cos
4
θ
+
2
sin
2
θ
cos
2
θ
13 - 4 \cos^4\theta + 2 \sin^2\theta \cos^2\theta
13
−
4
cos
4
θ
+
2
sin
2
θ
cos
2
θ
(3)
13
−
4
cos
2
θ
+
6
cos
4
θ
13 - 4 \cos^2\theta + 6 \cos^4\theta
13
−
4
cos
2
θ
+
6
cos
4
θ
(4)
13
−
4
cos
2
θ
+
6
sin
2
θ
cos
2
θ
13 - 4 \cos^2\theta + 6 \sin^2\theta \cos^2\theta
13
−
4
cos
2
θ
+
6
sin
2
θ
cos
2
θ
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