If 0\leq x<\pi/2, then the number of values of x for which  sin x - sin 2x + sin 3x = 0, is:

  • Option 1)

     

    3

  • Option 2)

     

    2

  • Option 3)

     

    1

  • Option 4)

     

    4

Answers (1)
A admin

 

Results from General Solution -

\sin \Theta = 0 \Rightarrow \Theta = n\pi

-

 

Given that 

\sin(x) - \sin(2x) + \sin(3x) = 0

From the concept

\\ \left[\sin (x) + \sin (3x)\right ] - \sin (2x) = 0 \\2\sin(2x)\cdot\cos(x) - \sin(2x) = 0 \\ \sin(2x)[2\cos(x) -1] = 0 \\ \sin(2x) = 0\; or \;\cos(x) = \frac{1}{2}

\Rightarrow x = 0, \frac{\pi}{3}


Option 1)

 

3

Option 2)

 

2

Option 3)

 

1

Option 4)

 

4

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