MCQ

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If $x$ satisfies the equation $\left( {\int\limits_0^1 {\frac{{dt}}{{{t^2} + 2t\cos \alpha  + 1}}} } \right)\,{x^2}$ $-$ $\,\left( {\int\limits_{ - 3}^3 {\frac{{{t^2}\sin 2t}}{{{t^2} + 1}}\,dt} } \right)\,x$ $-$ $2$  $ =$ $ 0 (0 < \alpha < \pi ), $ then the value $x$ is

• A
  $±$ $\sqrt {\frac{\alpha }{{2\sin \alpha }}} $
• B
  $±$ $\sqrt {\frac{{2\sin \alpha }}{\alpha }} $
• C
  $± $ $\sqrt {\frac{\alpha }{{\sin \alpha }}} $
• ✓
  $±$ $2\,\sqrt {\frac{{\sin \alpha }}{\alpha }} $