f(x) = cos x is monotonic decreasing under which one of the following conditions ?

Options

A. `0 lt x lt (pi)/(2)` only
B. `(pi)/(2) lt x lt pi` only
C. `0 lt x lt pi`
D. `0 lt x lt 2 pi`

Answer

C

Explanation

Given f(X) =cos x
`rarr f(X) =-sinx`
Now f(x)=0
`rarr -sinx =0`
`rarr -sin x =0`
`rarr sin x =0`
`rarr x= npi`
Clearly f(x) `lt` 0 when `0lt x ltpi`
Hence f(x) is decreasing when `0lt x lt pi`