Question

If a cos theta - b sibtheta = x and a sin theta + b cos theta = y, then prove that a square + b square = x square + y square

Answer 1

acos∅ -bsin∅ = x   and     asin∅+bcos∅ = y
 on squaring both the equations 
x² = a²cos²∅ + b²sin²∅ - 2abcos∅sin∅
y² = a²sin²∅ + b²cos²∅ + 2abcos∅sin∅
 on adding x² + y²
x²+y² = a²( sin²∅ + cos²∅) + b²(sin²∅ + cos²∅) - 2abcos∅sin∅ + 2abcos∅sin∅
x²+y² = a²+b²

Answer 2

Answer:

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