Question

If x=3 sin theta + 4 cos theta and y=3 cos theta - 4 sin theta then prove that x^2+y^2=25

Answer 1

Answer

Given that

X=3 sin theta+4 cos theta ,

Y=3 cos theta-4 sin theta

LHS,

X²+Y²=(3 sin theta+4cos theta)²+(3sin theta-4 sin theta)²

=9 sin² theta+16 cos² theta +24sin theta.cos theta +9cos²theta+16sin²theta-24sin theta.costheta

= 9( sin² theta + cos²theta)+16(sin² thet + cos² theta)

= 9+16

= 25.