Let `f,\ g,\ h` be real functions given by `f(x)=sinx` , `g(x)=2x` and `h(x)=cosx` . Prove that `fog=go(fh)dot`

Explanation

f, g and h are real functions given by `f(x)=sin x, g(x)=2 x and h(x)=cos x`
`
Rightarrow f o g(x)=f[g(x)]`
`
=f(2 x) ldots ldots . . . `[ Since, `g(x)=2 x ]`

`=sin 2 x . ldots ldots . . .` [ Since, `f(x)=sin x ]`
`
=2 sin x cdot cos x`
`
Rightarrow g of (x)=g o[f(x) cdot h(x)]`
`
=g(sin x cos x) ldots ldots . .[ Since, f(x)=sin x and h(x)=cos x ]`
`
=2 sin x cdot cos x . ldots ldots . . . [ Since, g(x)=2 x ]`
`
...