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