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Question
If `( cos theta + sin theta) = sqrt(2) sin theta , " prove that " ( sin theta - cos theta ) = sqrt(2) cos theta`
Solution
Given : `cos theta + sin theta = sqrt(2) sin theta`
We have `( sin theta + cos theta )^2 + (sin theta - cos theta )^2 =2(sin^2 theta + cos^2 theta )`
`= > ( sqrt(2) sin theta )^2 + ( sin theta - cos theta ) ^2 = 2 `
`= > 2 sin^2 theta + ( sin theta - cos theta ) ^2 = 2`
`= > ( sin theta - cos theta ) ^2 = 2-2 sin^2 theta `
`= > ( sin theta - cos theta ) ^2 =2(1- sin^2 theta)`
`= > ( sin theta - cos theta ) ^2 = 2 cos^2 theta`
`= > ( sin theta - cos theta ) = sqrt(2) cos theta`
Hence proved.
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