The value of cos2x for which the expression 1+ icosx/1-2icosx where( i root -1) is purely imaginary is
Answers
Given : (1 + i Cosx)/(1 - 2iCosx) is purely imaginary
To find : value of cos2x
Solution:
(1 + i Cosx)/(1 - 2iCosx)
= (1 + i Cosx) (1 + 2iCosx) / ( 1 - 2i Cosx )(1 + 2 i Cosx)
=(1 + 2i²Cos²x + iCosx + 2iCosx) / ( 1 - 4i²Cos²x)
= ( 1 - 2Cos²x + 3iCosx) / ( 1 + 4 Cos²x)
= (1 - 2Cos²x)/ ( 1 + 4 Cos²x) + i 3Cosx/( 1 + 4 Cos²x)
Puerly imaginary hence
(1 - 2Cos²x)/ ( 1 + 4 Cos²x) = 0
=> 1 - 2Cos²x = 0
=> - Cos2x = 0
=> Cos2x = 0
value of cos2x = 0 for which (1 + i Cosx)/(1 - 2iCosx) is purely imaginary
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