A value of θ for which 2+3isinθ 1-2isinθ is purely imaginary is (a) sin⁻¹ 3 4 (b) sin⁻¹ 1 3 (c) 3 (d) 6

Correct answer: (b) sin⁻¹ 1 3 Rationalising, the real part is (2-6sin²θ)/(1+4sin²θ); setting it to 0 gives sin²θ= 13, i.e. θ=sin⁻¹ 1 3. JEE Main 2016 · Complex Numbers — verified solution by the Vidaara Team.

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[JEE Main 2016] a value of theta for which 2 3i sin theta 1 2i sin theta

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

(a) $\sin^{-1}\frac{\sqrt3}4$
(b) $\sin^{-1}\frac1{\sqrt3}$
(c) $\frac\pi3$
(d) $\frac\pi6$

1 Answer

VAVidaara Admin ✓ Vidaara Team ✓ Accepted · 2d ago ▲ 0

Correct answer: (b) $\sin^{-1}\frac1{\sqrt3}$

Rationalising, the real part is $\frac{2-6\sin^2\theta}{1+4\sin^2\theta}$; setting it to $0$ gives $\sin^2\theta=\frac13$, i.e. $\theta=\sin^{-1}\frac1{\sqrt3}$.

JEE Main 2016 · Complex Numbers — verified solution by the Vidaara Team.

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