Question

Cos4π/15 cosπ/10 + din 4π/15 sinπ/10 va rog ajutati-ma

Answer 1

   
[tex]\displaystyle \bf\\ \text{Folosim formula:}\\ \cos(a-b) = \cos a \cdot \cos b + \sin a \cdot \sin b\\ \text{Transformam unghiurile din radiani in grade sexagesimale:}\\\\ \pi = 180^o\\\\ \frac{4\pi}{15} = \frac{4\times 180}{15} = 4\times 12 = 48^o\\\\ \frac{\pi}{10}=\frac{180}{10}=18^o\\\\ Rezolvare:\\\\ \cos \frac{4\pi}{15}\cdot \cos\frac{\pi}{10} + \sin\frac{4\pi}{15}\cdot \sin\frac{\pi}{10}=\\\\ =\cos 48^o \cdot \cos18^o + \sin 48^o\cdot \sin18^o=\\\\ =\cos (48^o-18^o)=\cos30^o=\frac{\sqrt{3}}{2} [/tex]