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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.
```

7 years ago

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```										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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