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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
cos 2 (cos@) + sin 2 (sin@)= cos 2 (cos@) + sin 2 (sin@) - sin 2 (cos@) + sin 2 (cos@)
= 1 + sin 2 (sin@) - sin 2 (cos@)
now it will be max. if the -ve term is zero as it is square so can't be +ve
hence cos(@) = 0 or sin(@) = 1
there fore its max. value is 1 + sin21
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