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If 0 < A1 < A2 < A3 < ........ < An < pi...

If `0 < A_1 < A_2 < A_3 < ........ < A_n < pi/2,` then prove that: `tanA_1 < (sinA_1+sinA_2+sinA_3+........+sinA_n)/(cosA_1+coaA_2+cosA_3+.......+cosA_n) < tan A_n`

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