Question

if xsin³Q+y cos³Q = sinQcosQ and xsinQ = y cosQ. prove that x²+y²=1​

Answer 1

Answer:

xsin³∅+ ycos³∅ = sin ∅cos∅

⇒ ( 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