If g is the inverse function of and f'(x) = sin x then prove that g'(x) = cosec (g(x))

Options

A. `cosec{g(x)}`
B. `sin {g(x)}`
C. `(1)/(sin{g(x)})`
D. none of these

Answer

C

Explanation

Since g is the inverse of function f. Therefore,
`fog(x)=x" "" for all "x`
`implies" "(d)/(dx)(fog(x))=(d)/(dx)(x)" "" for all "x`
`implies" "(d)/(dg(x)){f(g(x))}.g'(x)=1" "" for all "x`
`implies" "sin {g(x)}g'(x)=1" "" for all "x`
`implies" "g'(x)=(1)/(sin{g(x)})" ""for all "x`