lf `x=acostheta+bsintheta`, `y=asintheta-bcostheta` then show that `y^2(d^2y)/dx^2-x dy/dx+y=0`

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If x=acostheta+bsintheta,y=asintheta-bcostheta , show : y^(2)(d^(2)y)/(dx^(2))-x(dy)/(dx)+y=0 .

If x=acostheta-bsinthetaandy=asintheta+bcostheta , then show that : x^(2)+y^(2)=a^(2)+b^(2)

If acostheta+bsintheta=m and asintheta-bcostheta=n , then show that a^(2)+b^(2)=m^(2)+n^(2) .

If y=asin^(-1)x , then show that : (1-x^(2))(d^(2)y)/(dx^(2))-xdy/dx=0

If x/acostheta+y/bsintheta=1,x/asintheta-y/bcostheta=1 , then eliminate theta .

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If y=cos^(-1)x , then show that : (1-x^(2))(d^(2)y)/(dx^(2))-xdy/dx=0

If y=cot x show that (d^(2)y)/(dx^(2))+2y(dy)/(dx)=0

If x=acostheta+bsinthetaandy=bcostheta-asintheta ,then x^(2)+y^(2) is equal to