Bonjour,
x € (0;π/2) → CI
y € (π/2;π) → CII
sin x = 4/5
cos y = -3/5.
sin²x+cos²x = 1
16/25+cos²x = 1
cos²x = 9/25
cos x = 3/5.
sin²y+cos²y = 1
sin²y+9/25 = 1
sin²y = 16/25
sin y = 4/5.
sin(x-y) = sin x•cos y-sin y •cos x =
4/5•(-3/5)-4/5•3/5 = -12/25-12/25 = -24/25.
cos(x-y) = cos x•cos y+sin x•sin y =
3/5•(-3/5)+3/5•4/5 = -9/25+12/25 = 3/5.
cos(x+y) = cos x•cos y-sin x•sin y =
3/5•(-3/5)-4/5•4/5 = -9/25-16/25 = -25/25 = -1.
sin2y = 2siny•cos y = 2•4/5•(-3/5) = -8/5•3/5 = -24/25.
Succes!
