If x=asin~+bcos~ Y=acos-bsin~ Prove that x2+y2=a2+b2(~ symbolises teta and 2 is square of a;b;x;y)

If x=asin~+bcos~ Y=acos-bsin~ Prove that x2+y2=a2+b2(~ symbolises teta

1.	If x=asin~+bcos~ Y=acos-bsin~ Prove that x2+y2=a2+b2(~ symbolises teta and 2 is square of a;b;x;y)
Answer» According to the question,{tex}x^2 + y^2 = (asin\\theta\xa0+ bcos\\theta)^2 + (acos\\theta\xa0- bsin\\theta)^2{/tex}=\xa0{tex}a^2sin^2\\theta+b^2cos^2\\theta+2abcos\\theta sin\\theta+a^2cos^2\\theta+b^2sin^\\theta -2ab sin\\theta cos\\theta{/tex}= a2(sin2{tex}\\theta{/tex}\xa0+ cos2{tex}\\theta{/tex}) + b2(cos2{tex}\\theta{/tex}\xa0+ sin2{tex}\\theta{/tex}){tex}= a^2 + b^2{/tex} [{tex}\\because{/tex}\xa0sin2{tex}\\theta{/tex} + cos2{tex}\\theta{/tex}\xa0= 1].{tex}\\therefore{/tex}{tex}x^2 + y^2 = a^2 + b^2.{/tex}