If x=sin theta +b cos theta & y= a cos theta - b sin theta prove that x square + y square = a square + b sauare
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Step-by-step explanation:
x = aSinθ + bCosθ
y = aCosθ - bSinθ
x² + y² = (aSinθ + bCosθ)² + (aCosθ - bSinθ)²
= a²Sin²θ+ b²Cos²θ + 2abCosθSinθ + a²Cos²θ + b²Sin²θ - 2abCosθSinθ
= a²(Sin²θ + Cos²θ ) + b²(Cos²θ + Sin²θ )
= a² + b²
=R.H.S
Hence proved
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