x=a sin theta+b cos theta ,y=a cos theta -b sin theta,prove that x2+y2=a2+b2
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Step-by-step explanation:
let '* ● *' as theta
x = asin● + bcos●
y = acos● - bsin●
now
x² + y²
(asin● + bcos●)² + (acos● - bsin●)²
a²sin²● + b²cos²● + 2a bsin●cos● + a²cos● + b²sin²● - 2ab sin●cos●
a²sin²● + a²cos²● + b²cos²● + b²sin²●
a² (sin²● + cos²●) + b² (sin²● + cos²●)
*{ since sin²● + cos²● = 1}*
a² + b² proved
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