Sa se calculeze cos 30 grade + cos 60 grade + cos 120 grade + cos 150 grade
Rezolvare
Folosind formula cos x + cos (180 grade - x) = 0, putem scrie:
cos 30 grade + cos 150 grade =>
cos 30 grade + cos (180 grade - 30 grade) =.
cos 30 grade + cos 150 grade = 0
si
cos 60 grade + cos 120 grade =>
cos 60 grade + cos (180 grade - 60 grade) =>
cos 60 grade + cos 120 grade = 0
Astfel, avem:
cos 30 grade + cos 60 grade + cos 120 grade + cos 150 grade =>
(cos 30 grade + cos 150 grade) + (cos 60 grade + cos 120 grade) =>
0 + 0 = 0
Prin urmare, suma cosinusurilor este 0.
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