f, g and h are real functions given by f(x) = sin x, g(x) = 2x and

h(x) = cos x

To prove: fog=go(fh)

L.H.S

fog(x) = f(g(x))

= f(2x) = sin 2x

⇒ fog(x)=2sin x cos x ……(A)

R.H .S

go(fh)(x) = go(f(x).h(x))

= g(sin x cos x) = 2sin x cos x

go(fh)(x) = 2 sin x cos x ……(B)

from A and B

fog(x) = go(fh)(x)

Hence proved