$\newcommand{\tr}{\operatorname{tr}}$Let $K_1,K_2$ field extension of the field $F$ which are contained in a larger field $E$.

Prove that $\tr\deg(K_1K_2/F) \geqslant \tr\deg(K_i/F) ,i=1,2$ and

$$\tr\deg(K_1K_2/F) \leqslant \tr\deg(K_1/F)+\tr\deg(K_2/F)$$

$K_1K_2$ denotes the composite field of $K_1$ and $K_2$

Don't use the proposition:

$$F \leqslant K \leqslant E \Longrightarrow \tr\deg(E/F) = \tr\deg(E/K) + \tr \deg(K/F)$$

Can someone help me by giving a hint or something because i'm new to this subject?

Thank you in advance!