cos(0.5arctg(8/15)-0.5pi) - ?
arctg(8/15) =
x угол
tg(arctg(8/15)) = 8/15
значит:
a =
8 катет
b =
15 катет
c = √(8²+15²) = √(64+225) = √289 =
17 гипотенуза
х = arctg(8/15) угол между b и c
cos(0.5x-pi/2) = sin(0.5x)
=>
=> cos(0.5arctg(8/15)-0.5pi) = sin(0.5arctg(8/15))
sin(x) = sin(arctg(8/15)) = 8/17
cos(x) = cos(arctg(8/15)) = 15/17
Формулa половинного аргумента:
sin²(x/2) = (1 - cosx)/2
sin²(x/2) = (1 - 15/17)/2
sin²(x/2) = 1/17
sin(x/2) = ±1/√17
= ±√17/17
sin(x/2) = sin(0.5arctg(8/15)) = cos(0.5arctg(8/15)-0.5pi) =1/√17 = √17/17
cos(0.5arctg(8/15)-0.5pi) = 1/√17 = √17/17
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