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tan (A1+ A2+ A3+…+ An) = S1- S3 + S5 – S5+…/ 1- S2 + S4 – S6+…
where S1= tan A1+tan A2+tan A3+…+tan An,
S2 = tan A1 tan A2+ tan A2 tan A3+…And
Dear Sonam
we know
cos(A1+A2+....An) + i sin(A1+A2 +......An) =(cosA1 + i sinA1)(cosA2 + i sinA2)........(cosAn + i sinAn)
=cosA1 cosA2 .....cosAn (1+itanA1)(1+itanA2) .....(1+itanAn)
now multiply bracket terms
cos(A1+A2+....An) + i sin(A1+A2 +......An)
=cosA1 cosA2 .....cosAn {1+i(tanA1+tanA2 .......+tanAn) -(tanA1tanA2 + tanA2tanA3.....)-i(S3) +(S4) ........}
compair real and imaginary part
Sin (A1+ A2+ A3+…+ An) =cosA1cosA2 ....cosAn( S1- S3 + S5 – S5+…)
and
Cos(A1+ A2+ A3+…+ An) =cosA1cosA2 ....cosAn( 1- S2 + S4 – S6+…)
divide
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