if h(x) = f(g(x)) where h(x) = sinx and f(x) = cosx which of the following could define the function g

Question

options given

g(x) = √(x^2-1)

g(x) = √(1-x²)

g(x) = (π/2) +x

g(x) = (π/2) - x

g(x) = tanx

I tried doing it but cos^-1(sinx) isn't possible to do with what i know

Answer 1

h(x)=f(g(x))

sin x = cos [g(x)]

 

One of the cofunction identities says

sin A = cos (pi/2-A)

 

so g(x) must be pi/2-x

 

and you would have

sin x = cos (pi/2 - x)

 

like the identity says