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p=cos80∙cos40−sin80∙cos50

Răspuns :

P = cos(80°)∙cos(40°) − sin(80°)∙cos(50°)

= cos(80°)∙cos(40°) − sin(80°)∙cos(90°-40°)

║cos(90°-x) = sin(x)║

P = cos(80°)∙cos(40°) − sin(80°)∙sin(40°)

║cos(x+y) = cos(x)·cos(y) - sin(x)·sin(y)║

P = cos(80° + 40°)

= cos(120°)

= cos(2·60°)

║cos(2x) = cos²(x) - sin²(x)║

P = cos²(60°) - sin²(60)

= (1/2)² - (√3/2)²

= 1/4 - 3/4

= -1/2