Question

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
A. `P sub Q and Q-P ne phi`
B. `Q cancel(sub) P`
C. `P cancel(sub)Q`
D. `P = Q`

Answer 1

Correct Answer - D
`P = {theta: sin theta -costheta = sqrt(2) cos theta}`
`rArr cos theta (sqrt(2)+1) = sin theta`
` rArr tan theta = sqrt(2)+1`
`rArr Q = { theta : sin theta + cos theta} = sqrt(2) sin theta`
`rArr sin theta (sqrt(2) -1) = cos theta`
`rArr tan theta =(1)/(sqrt(2-1)) xx (sqrt(2)+1)/(sqrt(2)+1) = (sqrt(2)+1)`
`therefore P =Q`