Q. Let `P={theta:sin theta-cos theta=sqrt2 cos theta}` and `Q={theta:sin theta+cos theta=sqrt2 sin theta}` be two sets. then

Options

A. `P sub Q and Q-P=phi`
B. `Q cancelsub P`
C. `B cap C`
D. `A cap B capC`

Explanation

`theta in P`
`hArr sin theta - cos theta = sqrt(2)cos theta`
`hArr ( sin theta - cos theta)^(2)= 2cos ^(2)theta`
`hArr sin ^(2) theta + cos ^(2) theta - 2 sin theta -2 sin theta cos theta = 2 cos^(2)theta `
`hArr cos^(2) theta + 2 sin theta cos theta + sin ^(2) theta = 2 sin^(2) theta `
`hArr (cos theta + sin theta)^(2)= 2 sin ^(2) theta `
`hArr cos theta + sin theta = sqrt(2) sin theta`
`hArr theta in Q`.
hence P=Q.