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hornejada1c 2022-07-03 Answered
General formula for sin ( A 1 + A 2 + + A n )
I was wondering if there could be a general formula for this. Somehow, I managed to get (after some very small experimentation, so I'm not sure of what I'm going to say) that
sin ( A 1 + A 2 + + A n ) = cos A 1 cos A 1 cos A n ( i = 1 n tan A i 1 i < j < k n ( tan A i tan A j tan A k ) )
And I cannot prove it. Can anyone help me prove or disprove it?
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Answers (1)

Immanuel Glenn
Answered 2022-07-04 Author has 12 answers
It's not true for n=5:
( left side ) ( right side ) = sin ( A 1 ) sin ( A 2 ) sin ( A 3 ) sin ( A 4 ) sin ( A 5 )
I suspect that on the right side, for each k with 2 k + 1 n you need
( 1 ) k 1 i 1 < < i 2 k + 1 tan ( A i 1 ) tan ( A i 2 k + 1 )
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