Statement $-1:$ The number of common solutions of the trigonometric equations $2\,sin^2\,\theta - cos\,2\theta = 0$ and $2 \,cos^2\,\theta - 3\,sin\,\theta = 0$ in the interval $[0, 2\pi ]$ is two.
Statement $-2:$ The number of solutions of the equation, $2\,cos^2\,\theta - 3\,sin\,\theta = 0$ in the interval $[0, \pi ]$ is two.
Statement $-1$ is true; Statement $-2$ is true;Statement $-2$ is a correct explanation for statement $-1.$
Statement $-1$ is true; Statement $-2$ is true;Statement $-2$ is not a correct explanation for statement $-1.$
Statement $-1$ is false; Statement $-2$ is true.
Statement $-1$ is true; Statement $-2$ is false.
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The variable $x$ satisfying the equation $\left| {\sin \,x\,\cos \,x} \right| + \sqrt {2 + {{\tan }^2}\,x + {{\cot }^2}\,x} = \sqrt 3$ belongs to the interval