Calculate the value of $\sin a+\cos a$, knowing that $\sin a\cos a=0.48$ and $a$ belongs to $\left[\pi; \frac{3\pi}{2}\right]$?
What I did is: $$\sin a \cos a=0.48\ \ |\times 2$$
$$\sin 2a=0.96$$
$a= \dfrac{\arcsin \frac{24}{25}}{2} + \pi n$ or $a=\dfrac{\pi-\arcsin \frac{24}{25}}{2} + \pi n$
Now I don't know how to choose the right angles that belongs to the interval from the condition of the exercise! Thank you in advance!