Prove that this is a norm?

Question

I have a question:

I know the requirements of being a norm(the 3 requirements).I try to use them but,I don't know how to do.Can I get a litle help? Thank you.

Answer 1

For a), you can check that $$ \| 2\times (t\to \cos t) \| = 2^2 \neq 2 = |2| \times \| (t\to \cos t) \| $$

For b), check step by step the definition of the norm.