sin^2(pi\10)+sin^2(4pi\10)+sin^2(6pi\10)+sin^2(9pi\10)=
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Answer:
sin
2
10
π
+sin
2
10
4π
+sin
2
10
6π
+sin
2
10
9π
=sin
2
18
∘
+sin
2
72
∘
+sin
2
108
∘
+sin
2
162
∘
=sin
2
18
∘
+sin
2
(90
∘
−18
∘
)+sin
2
(90
∘
+18
∘
)+sin
2
(180
∘
−18
∘
)
=sin
2
18
∘
+cos
2
18
∘
+cos
2
18
∘
+sin
2
18
∘
=2sin
2
18
∘
+2cos
2
18
∘
=2(sin
2
18
∘
+cos
2
18
∘
)
=2×1
=2
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