`theta_(1),theta_(2),theta_(3)` are angles of `1^(st)` quadrant if `tan theta_(1) = cos theta_(1), tan theta_(2) = cosec theta_(2), cos theta_(3)=theta_(3)`. Which of the following is not true ?

Options

A. `theta_(1)lt theta_(2)`
B. `theta_(1)lt theta_(3)`
C. `theta_(3)lt theta_(1)`
D. `theta_(3)lt theta_(2)`

Answer

C

Explanation

`tan theta_(1)=cos theta_(1)lt 1`
`tan theta_(1)lt tan pi//4`
`therefore theta_(1) lt 45^(@)`
`tan theta_(2)=cosec theta_(2) gt 1`
`therefore tan theta_(2) gt tan 45^(@)`
`therefore theta_(2)gt 45^(@)`
For `cos theta_(3)=theta_(3)`, draw the graphs of y = cos x and y = x

From the graph, `theta_(1)lt theta_(3)`
`theta_(3)lt 45^(@)`
Thus, `theta_(1)lt theta_(3)lt theta_(2)`