Question

If a cos θ – b sinθ = x and a sinθ + b cosθ = y that a2 + b2 = x2 + y2.

Answer 1

Step-by-step explanation:

given,

x=acosθ-bsinθ

y=asinθ+bcosθ

from RHS

x²+y²=(acosθ-bsinθ)²+(asinθ+bcosθ)²

x²+y²=a²cos²θ+b²sin²θ-2absinθcosθ +a²sin²θ+b²sin²θ+2absinθcosθ

x²+y²=a²cos²θ+a²sin²θ+b²sin²θ+b²cos²θ

x²+y²=a²(cos²θ+sin²θ)+b²(sin²θ+cos²θ)

x²+y²=a²+b²