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JEE Main & Advanced JEE Main Paper (Held On 09-Jan-2019 Evening)

  • question_answer
    If \[0\,\,\le \,\,x\,<\,\,\frac{\pi }{2}\] , then the number of values of x for which \[\sin \,\,x-sin\text{ 2}x+sin\text{ }3x=0\] is [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

    A) 2     

    B)               4

    C)               3                                             

    D)               1

    Correct Answer: A

    Solution :

     \[sin\text{ }x-sin\text{ }2x+sin\text{ }3x=0\] \[x\,\in \,\left[ 0,\,\,\frac{\pi }{2} \right)\] \[\Rightarrow \] \[\left( sin\,3\,x+sin\,x \right)-sin\,2x=0\] \[\Rightarrow \,\,\,\,2sin2x.cos2x-sin2x=0\] \[\Rightarrow \,\,\,\,\,sin2x\,\left( 2cosx-1 \right)=0\] \[sin\text{ }2x=0~~~~and\text{ }cos\text{ }x=\frac{1}{2}\]     \[\text{x=0}\]                             \[\text{x=}\frac{\pi }{3}\]               two solutions                                       


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