Question

If x cos theta -y sin theta =a and x sin theta + y cos theta =b prove that x squae + y square = a square + b square

Answer 1

Solution:

• x cosØ - y sin Ø = a ...(1)
• x sinØ + y cos Ø = b...(2)

Square (1) and (2) and add them we get,

x²cos²Ø + y²sin²Ø + x²sin²Ø + y²cos²Ø = a² + b²

=> (x² + y²) (sin²Ø + cos²Ø) = a² + b²

=> x² + y² = a² + b²

Hence, proved.