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if the expression [sin(x/2) + cos(x/2) - itan(x/2)]/{1+i2sin(x/2)} is real, then the set of all possible values of x is _________
Dear raman
[sin(x/2) + cos(x/2) - itan(x/2)]/{1+i2sin(x/2)}
multiple 1-21sin(x/2) in nominator and denomenator and equate coefficient of i to zero
-tanx/2 -2sinx/2(sinx/2 +cosx/2) =0
or sinx/2 ( 1+ 2cosx/2((sinx/2 +cosx/2)) =0
or sinx/2(2+sinx/2 +cosx/2)=0
term in the bracket can not equal to zero
so sinx/2 =0
x/2 =n∏
x=2n∏ for n any intiger
All the best. Regards,Askiitians ExpertsBadiuddin
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