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Question
If x cos A + y sin A = m and x sin A – y cos A = n, then prove that : x2 + y2 = m2 + n2
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Solution
m2 + n2
= (x cos A + y sin A)2 + (x sin A – y cos A)2
= x2 cos2 A + y2 sin2 A + 2xy sin A cos A + x2 sin2 A + y2 cos2 A – 2xy sin A cos A
= x2 (cos2 A + sin2 A) + y2 (cos2 A + sin2 A)
= x2 + y2
Hence, x2 + y2 = m2 + n2
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