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1)

The number  of solution of sinx +sin 3x+sin 5x=0  in the interval  [π2,3π2]  is 


A) 2

B) 3

C) 4

D) 5

Answer:

Option B

Explanation:

 We have,

 sinx +sin 3x+sin 5x=0

     sinx+sin5x+sinx=0

  2sin3xcos2x+sin3x=0

    sin3x(2cos2x+1)=0

   sin3x=0  or cos2x=12=cos2π3

3x=nπ  or   2n=2nπ±2π3

    x=nπ3   or   x=nπ±π3  

  But, it is given that

xϵ[π2,3π2]

      x=2π3,π,4π3

    Number of solutions is 3.