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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
S3 = tan A1 tan A2 tan A3 + tan A2 tan A3 tan A4 +…```
7 years ago

147 Points
```										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
tan (A1+ A2+ A3+…+ An)  = S1- S3 + S5 – S5+…/ 1- S2 + S4 – S6+…
Please feel free to post as many doubts on our discussion forum as you can.If you find any question Difficult to understand - post it here and we will get you the answer and detailed  solution very  quickly. We are all IITians and here to help you in your IIT JEE preparation.All the best. Regards,Askiitians ExpertsBadiuddin
```
7 years ago
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