The real part of ${\left( {1 - \cos {\rm{\theta }} + 2i\sin {\rm{\theta }}} \right)^{ - 1}}$ is

$\frac{1}{{5 + 3\cos {\rm{\theta }}}}$

$\frac{1}{{3 + 5\cos {\rm{\theta }}}}$

$\frac{1}{{5 - 3\cos {\rm{\theta }}}}$

$\frac{1}{{3 - 5\cos {\rm{\theta }}}}$

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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Application +4 | -1

The real part of

{\left( {1 - \cos \mathrm{\theta } + 2i\sin \mathrm{\theta }} \right)^{ - 1}}

View answer and explanation

Correct option: D

\frac{1}{{5 + 3\cos \mathrm{\theta }}}

The correct answer is D (

\frac{1}{{5 + 3\cos \mathrm{\theta }}}}

) because after rationalizing and simplifying, the real part of the given expression is

\frac{1}{{5 + 3\cos \mathrm{\theta }}}}

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