If `x = sin 130^(@) cos 80^(@), y = sin 80^(@) cos 130^(@), z = 1+xy`, which one of the following is true ?

Options

A. `x gt 0, y gt 0, z gt 0`
B. `x gt 0, y lt 0, 0 lt z lt 1`
C. `x gt 0, y lt 0, z gt 1`
D. `x lt0, y lt 0, 0 lt z lt 1`

Answer

B

Explanation

`x sin 130^(@)cos 80^(@), y = sin 80^(@) cos 130^(@)`
`rArr x = cos 40^(@)cos 80^(@), y =-sin 80^(@) sin 40^(@)`
So, `x gt 0` and `y lt 0` and `xy lr 0`
Now, `z =1+xy rArr 0 lt x lt 1`.