For any real $\theta$ the maximum value of $$\cos^2(\cos\theta) + \sin^2(\sin\theta)$$
B. $1 + \sin^21$
C. $1 + \cos^21$
D. does not exist
I tried it by converting the whole expression into $\sin$ but getting nowhere with that.
$$1-\sin^2(\cos\theta) + \sin^2(\sin\theta)$$
Now since 1 is constant therefore, $$[\sin^2(\cos\theta) + \sin^2(\sin\theta)]$$ should be minimum but I don't know how to minimize it.
Also is there a way to think about it's solution graph.
I have to solve this without using calculus. Kindly help.