Question

x=a sin theta+b cos theta ,y=a cos theta -b sin theta,prove that x2+y2=a2+b2

Answer 1

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