If `(sin theta, cos theta) and (3,2)` lie on the same side of the line `x+y=1,` then `theta` lies between

Options

A. `0, pi/2`
B. `0,pi`
C. `pi/4,pi/2`
D. `0,pi/4`

Answer

D

Explanation

Given points are `(sin theta , cos theta) and (3,2)` and a line is x+y-1=0
On substituting (3,2) in Eq (i) we get
3+2 -1 gt 0
On substituting `(sin theta, cos theta ) ` In Eq (i) We get
`sin theta + cos theta -1 gt 0`
The points ` sin theta , cos theta and (3,2)` lies on the same side of x +y -1 =0]
` sin theta + cos theta gt 1 `
` Rightarrow sqrt2 [ sin ( theta + pi/4)] lt 1`
` Rightarrow sin (theta + pi/4) lt 1/sqrt2 = sin (pi/4)`
` Rightarrow pi/4 lt theta + pi/4 lt pi/2`
`Rightarrow 0 lt theta lt pi/4`