A value of heta \, for which {{2 + 3i\sin heta \,} \over {1 - 2i\,\,\sin \, heta \,}} is purely imaginary, is :

Question

A value of 	heta \, for which {{2 + 3i\sin 	heta \,} \over {1 - 2i\,\,\sin \,	heta \,}} is purely imaginary, is :

Accepted Answer

Answer: B. {\sin ^{ - 1}}\left( {{1 \over {\sqrt 3 }}} ight)\, Rationalizing the given expression {{\left( {2 + 3i\sin 	heta } ight)\left( {1 + 2i\sin 	heta } ight)} \over {1 + 4{{\sin }^2}	heta }} For the given expression to be purely imaginary, real part of the above expression should be equal to zero. \Rightarrow {{2 - 6{{\sin }^2}	heta } \over {1 + 4{{\sin }^2}	heta }} = 0 \Rightarrow {\sin ^2}	heta = {1 \over 3} \Rightarrow \sin 	heta = \pm {1 \over {\sqrt 3 }}

A value of $$\theta \,$$ for which $${{2 + 3i\sin \theta \,} \over {1 - 2i\,\,\sin \,\theta \,}}$$ is purely imaginary, is :

Answer

Explanation

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