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ISI2019-MMA-8

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For $0 \leq x < 2 \pi$, the number of solutions of the equation

$$\sin^2x + 2 \cos^2x + 3\sin x \cos x = 0$$

is

  1. $1$
  2. $2$
  3. $3$
  4. $4$
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The equation reduces to

$(\sin x+ \cos x)(\sin x + 2 \cos x) = 0$

$\implies \tan x = -1$ and $ \tan x = -2 $

$\tan x$ has a period of $\pi$, which means it takes each value twice in an interval of $2\pi$ . So the answer is $4$
$D$ is correct answer.
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