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Grade: 12
        

Ques2) For any real @, show that the max value of cos 2 (cos@) + sin 2 (sin@) is 1+sin 2 1.

10 years ago

Answers : (1)

pratham ashish
9 Points
							Hi,
 
Let cos@ =A
   
    sin@ =B 

   then  cos ^2 (A) + sin^2 (B)= 1 - sin^2(A)+sin^2(B)

                               =  1- {sin^2(A)-sin^2(B)}

                               =  1-  {sin(A)+sin(B)}{sin(A)-sin(B)}

                                = 1- sin(A+B)sin(A-B)

                                = 1 + sin(B+A)sin(B-A)


     value of any  X*Y is max when X=Y  


              hence max  value of    sin(B+A)sin(B-A)  when sin(B+A)= sin(B-A)  
                        
                                                 =>  B-A = B +A
                                                 =>  A = 0 

this will happen when @  = 90 => cos@ = 0 & sin@ = 1
  
                         cos ^2 (A) + sin^2 (B) = 1 + sin(B+A)sin(B-A)= 1 + sin^2(1)

 I think this is sufficient

Good Luck & Enjoy 
                          

                    
						
10 years ago
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