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Confused! kindly explain, - Trigonometry - JEE Main-8

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)
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V Vakul

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

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