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