If $a = \cos {\rm{\theta }} + i\sin {\rm{\theta }},{\rm{\;then\;}}\frac{{1 + a}}{{1 - a}}$ is equal to

$i\cot \frac{{\rm{\theta }}}{2}$

$\cot \frac{{\rm{\theta }}}{2}$

$i\tan \frac{{\rm{\theta }}}{2}$

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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Application +4 | -1

a = \cos \mathrm{\theta } + i\sin \mathrm{\theta },\mathrm{\;then\;}\frac{{1 + a}}{{1 - a}}

is equal to

View answer and explanation

Correct option: C

i\cot \frac{\mathrm{\theta }}{2}

Option C (

i\cot \frac{\mathrm{\theta }}{2}

) is correct because it is the simplified form of the given expression using Euler's formula and trigonometric identities.

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