[JEE Advanced 2007] the number of theta in 0 2 pi satisfying both 2 sin 2 theta
The number of $\theta\in[0,2\pi]$ satisfying both $2\sin^2\theta-\cos2\theta=0$ (i.e. $4\sin^2\theta=1$) and $2\cos^2\theta-3\sin\theta=0$ is
(a) zero
(b) one
(c) two
(d) four
1 Answer
VAVidaara Admin
✓ Vidaara Team
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· 2d ago
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Correct answer: (c) two
Second equation: $2(1-\sin^2\theta)-3\sin\theta=0\Rightarrow\sin\theta=\frac12$. This also satisfies $\sin^2\theta=\frac14$ from the first. In $[0,2\pi]$, $\sin\theta=\frac12$ gives $\theta=\frac\pi6,\frac{5\pi}6$ — two.
JEE Advanced 2007 · Trigonometry — verified solution by the Vidaara Team.
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