Question

Prove que para |x|≤ 1, tem-se:


arc sen x + arc cos x = π/2

Answer 1

g(x)=arc sen x + arc cos x = π/2 

podemos testar  para varios valores de x
p/x=0

g(0)=arc sen 0 + arc cos 0 = π/2 
 g(0)=     0      +   π/2       = π/2 

p/x=1
g(1)=arc sen 1 + arc cos 1 = π/2 
g(1)=     π/2     +     0     =   π/2 

p/x=-1

g(1)=arc sen -1 + arc cos -1= π/2 
g(1)=     -π/2     +     π     =   π/2 

pronto