If `e^(-pi//2) lt theta lt pi //2 ` ,then =

Options

A. cos (log `theta) gt ` log (cos `theta`)
B. cos (log `theta) lt` log (cos `theta`)
C. cos (log `theta`) = log (cos `theta`)
D. None of these

Answer

A

Explanation

since `e^(-pi//2) lt theta lt pi//2`
`implies "log" e^(-pi//2) lt "log" theta lt "log" pi//2`
`implies -(pi)/(2) lt "log" theta lt "log" (pi)/(2) lt 1 lt pi//2`
i.e., `-(pi)/(2) lt "log" theta lt (pi)/(2)`
But 0`lt` cos `theta lt 1`
so ,log (cos `theta) lt` log (1)
`implies ` log (cos `theta) lt 0`
Hence cos (log `theta) lt ` log (cos `theta`)