[tex]\displaystyle\\
f(x)= \sin\left(\frac{2x}{3}\right)+\cos\left( \frac{3x}{2} \right) \\\\\\
f\left( \frac{\pi}{2} \right)= \sin\left( \frac{2\cdot \dfrac{\pi}{2}}{3} \right) + \cos\left( \frac{3\cdot \dfrac{\pi}{2}}{2} \right)=\\\\\\
= \sin\left( \frac{\pi }{3} \right) + \cos\left( \frac{3\pi}{4} \right)=\\\\\\
= \sin 60^o + \cos 135^o =\\\\
= \frac{ \sqrt{3} }{2} + \cos(180 - 45)=\\\\
= \frac{ \sqrt{3} }{2} - \cos 45=\\\\
= \frac{ \sqrt{3} }{2}-\frac{\sqrt{2}}{2}=\boxed{\frac{\sqrt{3}-\sqrt{2}}{2}}
[/tex]
Raspuns corect: a)
