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The number of integral values of a for which the equation cos2x+asinx=2a-7 possesses a solution is----------------

The number of integral values of a for which the equation cos2x+asinx=2a-7 possesses a solution is----------------


 

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1 Answers

Badiuddin askIITians.ismu Expert
148 Points
12 years ago

Dear sri

cos2x+asinx=2a-7

1-2sin2x + asinx =2a-7

2sin2x -asinx +2a-8 =0

 discrimnant =a2 -8(2a-8)

                         =a2 -16a +64

                           =(a-8)2

 

so sinx  = [a±|a-8|]/4

                  =(a-4)/2 , 2

  so  only  (a-4)/2 is possible 

           -1≤(a-4)/2 ≤1

           -2 ≤a-4 ≤2

            2 ≤a ≤ 6

  so  solution is  a =2,3,4,5,6

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