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

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

Grade:12

2 Answers

Badiuddin askIITians.ismu Expert
148 Points
14 years ago

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

    

Varun L
11 Points
5 years ago
bro,
i have a doubt like if we substitute the answer u r getting i.e n(pi) + (pi)/4
let us take n=0
x=pi/4
2^(1/21/2)+2^(1/21/2) = 2*2^(1/21/2)
                                 =2^(1+1/21/2)
 
Then how on earth is it a solution

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