Question

The range of `f(x)=[sinx|[cosx[tanx[secx]]]],x in (0,pi/4),w h e r e` [.] denotes the greatest integer function less than or equal to `x ,` is (0,1) (b) `-{1,0,1}` `{1}` (d) none of these

Answer 1

Given
`f(x)=[sin x+[cosx+[tanx+[secx]]]]`
`=[sin+p], " where " P=[cosx +[tanx+[secx]]]]`
`=[sinx]+p,` (as p is an integer)
`=[sinx]+[cosx+[tanx+[secx]]]]`
`=[sinx]+[cosx]+[tanx]+[secx]`
Now, for ` x in(0,pi//4),sinx in(0, (1)/(sqrt(2))), cosx in((1)/(sqrt(2)),1), `
`tanx in(0,1), secx in (1, sqrt(2))`
or `[sinx]=0,[cosx]=0,[tanx]=0, " and " [secx]=1`
Therefore, the range of f(x) is 1.