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iit jee Grade: 12
        

find the most general solutions for 2sin x + 2cos x = 21 - (2)-1/2

7 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert
147 Points
										

Dear


2sin x + 2cos x = 21 - (2)-1/2


 


As we know AM ≥GM


                 (2sin x + 2cos x)/2≥(2sin x  2cos x )1/2    equality occur when 2sin x = 2cos x


       or   (2sin x + 2cos x)/2≥(2sin x +cosx )1/2


  mimimum value occur sinx+cosx=-√2


      or   (2sin x + 2cos x)/2≥(2-√2 )1/2


     or   (2sin x + 2cos x)21-1/√2 


  so for solution equality should be occur


ie   2sin x = 2cos x


   sinx =cosx


 tanx =1


  x=n∏ +∏/4


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Badiuddin


    

7 years ago
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