Mariasmileforeverask
a fost răspuns

Sa se arate ca: cos[tex] \frac{2 \pi }{7} [/tex] + cos[tex] \frac{4 \pi }{7} [/tex] + cos[tex] \frac{6 \pi }{7} [/tex] = -[tex] \frac{1}{2} [/tex]

Răspuns :

Cristinatibulcaask
sin[tex]( sin\frac{ \pi }{7} *cos \frac{2 \pi }{7} + sin\frac{ \pi }{7} *cos \frac{4 \pi }{7}+ sin\frac{ \pi }{7} *cos \frac{6 \pi }{7})/sin\ \frac{ \pi }{7} [/tex]
se foloseste formula sin A+ sin B=1/2(sin(A-B)+sin(A+B))⇒
(sin(π/7-2π/7)+sin(π/7+2π/)+sin(π/7-4π/7)+sin (π/7+4π/7)+sin(π/7-6π/7)+sin(π/7+6π/7))/2sinπ/7=
(sin(-π/7)+sin(3π/7)+sin(-3π/7)+sin5π/7+sin(-5π/7)+sin 7π/7)/2sinπ/7=
(sin(-π/7)+sinπ)/2sinπ/7=(sin(-π/7)+0)/2sinπ/7=-1/2

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