Question

If x = 3 sinθ + 4 cos θ and y = 3 cos θ − 4 sin θ then prove that x 2 + y 2 = 25

Answer 1

Step-by-step explanation:

x²= (. 3 sinθ + 4 cos θ )²

= 9sin²θ + 16cos²θ + 24sinθcosθ_____(i)

similarly

y²= 16sin²θ + 9cos²θ - 24sinθcosθ_____(ii)

now adding (i) and (ii) equations

x²+y²= 9sin²θ + 16cos²θ + 24sinθcosθ +

16sin²θ + 9cos²θ - 24sinθcosθ

x² + y²= 9( sin²θ + cos²θ ) +16( sin²θ + cos²θ )

x²+y²= 9+16

x²+y²= 25

HENCE PROVED