Question

Care este răspunsul la Cos 7 pi supra 12

Answer 1

[tex]\cos{\frac{7 \pi }{12}=\cos{(\frac{3 \pi }{12}+\frac{4 \pi }{12})}=\cos(\frac{ \pi }{4}+\frac{ \pi }{3})}\\ Aplicam\ formula:cos(a+b)=cosa\cdot cosb-sina\cdot sinb\\ cos\frac{\pi}{4}\cdot \cos{\frac{\pi}{3}}-sin\frac{\pi}{4}\cdot sin\frac{\pi}{3}=\frac{\sqrt{2}}{2}\cdot\frac{1}{2}-\frac{\sqrt{2}}{2}\cdot \frac{\sqrt{3}}{2}=\frac{\sqrt{2}}{4}-\frac{\sqrt{6}}{4}=\\ \boxed{\boxed{\frac{\sqrt2-\sqrt6}{4}}}[/tex]