KVPY Sample Paper KVPY Stream-SX Model Paper-21

  • question_answer
    The number of roots of the equation, \[\sin x+2\sin 2x=3+\sin 3x\] is:

    A) 0

    B) 1

    C) 2

    D) infinite

    Correct Answer: A

    Solution :

    \[(sinx-\sin 3x)+2sin2x=3\]\[\Rightarrow \]\[-\,2\sin x\cos 2x+2\sin 2x=3\]\[\Rightarrow \]\[2\sin x\cos 2x-2\sin 2x+3=0\]
    \[2\sin x\cos 2x-2\sin 2x+(si{{n}^{2}}x+{{\cos }^{2}}x)+\]\[(si{{n}^{2}}2x+{{\cos }^{2}}2x)+1=0\]\[\Rightarrow \]\[{{(1-sin2x)}^{2}}+{{(\sin x+\cos 2x)}^{2}}+{{\cos }^{2}}x=0\]
    \[\Rightarrow \]No root

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