Correct question is:

Find biggest among sin 1 + cos 1, √(1 + sin 2), √(sin 1) + √(cos 1)

Solution:

Here, √(1 + sin 2) = √(sin² 1 + cos² 1 + 2*sin 1 * cos 1) = |sin 1 + cos 1|

So, √(1 + sin 2) = sin 1 + cos 1    

Now, √(sin 1) > sin 1 and cos 1 > cos 1 

This is because sin 1, cos 1, √(sin 1), √(cos 1) ∈ (0, 1)       {Here 1^c = 57^° }

So, sin 1 + cos 1 = √(1 + sin 2) < √(sin 1) + √(cos 1)