If $A=\sin^{20}\theta +\cos^{48}\theta $ then identify the correct option. 
If $A=\sin^{20}\theta +\cos^{48}\theta $, then for all values $\theta$
  a) $A\geq 1$
  b) $ 0< A\leq 1$
  c) $1<A< 3$
  d) None of these

$0 \leq \sin^{20}\theta \leq 1$
$0 \leq \cos^{48}\theta \leq 1 $
So I think it is $d.)$ , but I am confused.
I look for a short and simple way.
I have studied maths upto $12$th grade.

Hint:
You should know that
\begin{align}
0 \leq \sin^{20}\theta \leq \sin^2\theta \leq 1\\
0 \leq \cos^{48}\theta \leq \cos^2\theta \leq 1
\end{align}
So
$$0\leq \sin^{20}\theta + \cos^{48}\theta \leq \sin^2\theta + \cos^2\theta $$
And the last sum is $1$.
