DS 2 - PCSI-PSI AUX ULIS

z, z0∈C,|z|+|z0|≤|z+z0|+|z−z0|
∀x∈[−1,1],cos(Arcsin(x)) = √1−x2
Arcsin ]−1,1[
∀x∈]−1,1[, Argth(x) = 1
2ln 1 + x 1−x
f[0, π]
∀x∈[0, π], f(x) = sin(x)
√5−4 cos x.
f f0(x) cos x−1
2
f[0, π]
g[0, π]
∀x∈[0, π], g(x) = Arccos 4−5 cos(x)
5−4 cos(x).
g[0, π]
x∈[0, π] cos(g(x)) sin(g(x))
g0(x)x∈]0, π[
cos g(x)g[0, π]
∀x∈[0, π]g(g(x)) = x
(Γ) g
xh0,π
3i
zhπ
3, πi
f(z) = f(x)
z=g(x)
z, z0∈C,|z|+|z0| ≤ |z+z0|+|z−z0|
∀x∈[−1,1],cos(Arcsin(x)) = √1−x2
Arcsin ]−1,1[
∀x∈]−1,1[, Argth(x) = 1
2ln 1 + x 1−x
f[0, π]
∀x∈[0, π], f(x) = sin(x)
√5−4 cos x.
f f0(x) cos x−1
2
f[0, π]
g[0, π]
∀x∈[0, π], g(x) = Arccos 4−5 cos(x)
5−4 cos(x).
g[0, π]
x∈[0, π] cos(g(x)) sin(g(x))
g0(x)x∈]0, π[
cos g(x)g[0, π]
∀x∈[0, π]g(g(x)) = x
(Γ) g
xh0,π
3i
zhπ
3, πi
f(z) = f(x)
z=g(x)