1.

If x = a cos θ + sin θ. y = a sin θ – b cos θ. Show that x2 + y2 = a2 + b2 

Answer»

Consider x2 = (acosθ + bsin θ)2 

⇒ x2 = a2cos2θ + 2abcosθsinθ + b2sin2θ …….(1) 

Again consider y2 = (asinθ – bcosθ)2 

⇒ y2 = a2sin2θ – abcosθ sinθ + b2cos2θ …….. (2) 

(1) + (2) ⇒ x2 + y2 = a2 + b2 


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