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The equation y=\sin x\sin \left ( x+2 \right )-\sin ^{2}\left ( x+1 \right ) represents a straight line lying in : 

 


 

  • Option 1)

    first, third and fourth quadrants 

  • Option 2)

    third and fourth quadrants only

  • Option 3)

    first, second and fourth quadrants

  • Option 4)

    second and third quadrants only

 

Answers (1)

y=\sin x\sin \left ( x+2 \right )-\sin ^{2}\left ( x+1 \right )

2y=2\sin x\sin \left ( x+2 \right )-2\sin ^{2}\left ( x+1 \right )

      =\cos 2-\cos \left ( 2x+2 \right )-\left ( 1-\cos \left ( 2x+2 \right ) \right )

     =\cos 2-1

y=\frac{\cos 2-1}{2}=-\sin^21

 


Option 1)

first, third and fourth quadrants 

Option 2)

third and fourth quadrants only

Option 3)

first, second and fourth quadrants

Option 4)

second and third quadrants only

Posted by

Vakul

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