Question

If x = 3sin@+4cos@ and y= 3cos@-4sin@ then prove that x2+ y2=25

Answer 1

Step-by-step explanation:

x²+y²

= (3Sin@+4Cos@)² + (3Cos@-4Sin@)²

= (9Sin²@ + 16Cos²@ + 24Sin@*Cos@) + (9Cos²@ + 16Sin²@ - 24Sin@*Cos@)

= 9(Sin²@+Cos²@)+16(Cos²@+Sin²@) + 0

= 9*1 + 16*1 + 0

= 9+16 = 25