1.

If `x=a sin theta+b cos theta and y=a cos theta -b sin theta, " prove that " x^(2)+y^(2)=a^(2)+b^(2).`

Answer» We have
` x^(2) + y^(2) = (a sin theta + b cos theta)^(2) + (a cos theta - b sin theta)^(2) `
` = a^(2)(sin^(2)theta + cos^(2)theta ) + b^(2)(cos^(2)theta + sin^(2)theta) `
`= a^(2) + b^(2) " " [ because sin^(2)theta + cos^(2)theta =1]. `
Hence, ` x^(2) + y^(2) = a^(2) + b^(2). `


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