Question

If x=a sina+b cos A
and y=a cosA-b sin A
then x² + y2 =
​

Answer 1

x^2=a^2sin^2A+2absinAcosA

+b^2cos^2A

y^2=a^2cos^2A-2abcosAsinA

+b^2sin^2A

x^2+y^2=a^2sin^2A+b^2cos^2A+

a^2cos^2A+b^2sin^2A

=a^2(sin^2A+cos^2A)+

b^2A(sin^2A+cos^2A)

x^2+y^2 =a^2+b^2