QJEEM16Mab5a3: JEE Main 2016 Mathematics - Class 11 JEEM16Mab5a3 Solution: A value of θ for which 2 + 3 i sin ⁡ θ 1 − 2 i sin θ is purely…

Question

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A value of

θ

for which

\frac{2 + 3 i \sin θ}{1 - 2 i \sin θ}

is purely imaginary, is :

Accepted Answer

Rationalizing the given expression

\frac{(2 + 3 i \sin θ) (1 + 2 i \sin θ)}{1 + 4 \sin^{2} θ}

For the given expression to be purely imaginary, real part of the above expression should be equal to zero.

\Rightarrow \frac{2 - 6 \sin^{2} θ}{1 + 4 \sin^{2} θ} = 0

\Rightarrow \sin^{2} θ = \frac{1}{3}

\Rightarrow \sin θ = \pm \frac{1}{\sqrt{3}}

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