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Let P={theta : sin theta -cos theta =sqr...

Let `P={theta : sin theta -cos theta =sqrt2cos theta}` and `Q={theta : sin theta +cos theta =sqrt2 sin theta}` be two sets . Then :

A

`PsubQ and A - P ne phi`

B

`QcancelsubP`

C

`PcancelsubQ`

D

P = Q

Text Solution

Verified by Experts

The correct Answer is:
D
`P:sintheta-costheta=sqrt(2)costhetaimpliestantheta=sqrt(2)+1`
`Q:sintheta+costheta=sqrt(2)sinthetaimpliestantheta=(1)/(sqrt(2)-1)=sqrt(2)+1`
`therefore P = Q`
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