Question

If xsin³ø+ycos³ø=sinø and xsinø=ycosø, prove that x²+y²=1

Answer 1

Heyaa user !


We need to use the given condition

but we are given that -

xsin³∅+ ycos³∅ = sin ∅cos∅

we can write it as

⇒ ( xsin∅ ) sin²∅ + ( ycos∅ ) cos ²∅ = sin∅ cos ∅

⇒ xsin∅ ( sin∅ ) ²+ ( xsin∅ ) ²cos∅ = sin∅cos∅

{ ∵ xsin∅ = ycos∅ }

⇒ xsin∅ [ sin∅² + cos∅ ²] = sin∅ cos∅

⇒ xsin∅ = sin∅cos∅

or x = cos∅

Now ,

xsin∅ = ycos∅

⇒ cos∅.sin∅ = ycos∅

⇒ y = sin∅

Hence x² + y² = cos² + sin² = 1


Hope this would help you !!