यदि `cos theta + sin theta = sqrt(2) cos theta` हो, तो दर्शाइए कि - `cos theta - sin theta = sqrt(2)sin theta`.

Explanation

चूँकि `" " cos theta + sin theta = sqrt(2) cos theta`
`rArr " " sin theta = sqrt(2) cos theta - cos theta = cos theta (sqrt(2)-1)`
`rArr " " cos theta = (sin theta)/(sqrt(2)-1)`
`rArr " " cos theta = (sin theta (sqrt(2)+1))/((sqrt(2)-1)(sqrt(2)+1))=(sin theta (sqrt(2)+1))/(2-1)`
`rArr " " cos theta = sqrt(2) sin theta + sin theta`
`rArr " " cos theta - sin theta = sqrt(2) sin theta`
`rArr " " L.H.S. = R.H.S. " "` इति सिद्धम्