$$ 4^{sin(x)}+4^{-sin(x)}=\frac{5}{2} $$
$$ (4^{sin(x)})^{2}-\frac{5}{2} \times 4^{sin(x)}+1=0 $$
$$ \bigtriangleup = \frac{9}{4} \Rightarrow 4^{sin(x)}=2 یا 4^{sin(x)}= \frac{1}{2} $$
$$\color{red}{sin(x)= \mp \frac{1}{2} \Rightarrow x=2k \pi \mp \frac{ \pi }{6} \vee x=2k \pi + \pi \mp \frac{ \pi }{6}}$$
یا میتوان نوشت:
$$ \color{green}{ x=k \pi \mp \frac{ \pi }{6}} $$
