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Tushar Watts Grade: 12
        

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

7 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


7 years ago
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