1.

The real value of `theta` for which the expression `(1 + icos theta)/(1 - 2i cos theta)` is real number isA. `npi+(pi)/(4)`B. `npi+(-1)^(2)(pi)/(4)`C. `2npipm(pi)/(2)`D. None of these

Answer» Correct Answer - C
Given expression = `(1+icostheta)/(1-2icostheta)=((1+icostheta)(1+2icostheta))/((1-2icostheta)(1+2icostheta))`
`=(1+icostheta+2icostheta+2i^(2)cos^(2)theta)/(1-4i^(2) cos^(2)theta)`
`=(1+3icostheta-2cos^(2)theta)/(1-4 cos^(2)theta)`
For real value of `theta, (3costheta)/(1+cos^(2)theta)=0`
`rArr 3costheta= 0`
`rArr costheta = cos(pi)/(2)`
`rArr theta= 2npipm(pi)/(2)`


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