Question

If x = 3sinX + 4cosX and Y =3cosX -4sinX prove that x²+ y²=25.

Whomsoever will ans correctly I'll make you brainliest.

‍♀️​

Answer 1

Step-by-step explanation:

Given equation

X=3 sinx+4cosx

Y=3cosx-4sinx

RHS=x^2+y^2

=(3sinx+4cosx)^2+(3cosx-4sinx)^2

=9sin^2 x+16cos^2 x+9cos ^2x-16sin^2 x =9sin^2x+9cos^2 x+16cos^2 x-16sin^2 x

=9(sin^2x+cos ^2 x)+16(cos^2 x- sin^2x)

=9+16

=25

=RHS