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Answer to Question #4208 in Trigonometry for esha

Question #4208
2cosA-sinA=x and cosA-sinA=y. Prove that 2x*x+y*y-2xy=5
Expert's answer
2cosA - sinA = x
cosA - sinA = y.

2x*x+y*y-2xy= 2* (2cosA - sinA)*(2cosA - sinA) + (cosA - sinA)(cosA - sinA) - 2 *(2cosA - sinA)* (cosA - sinA) =
= 2 (4 cos2A - 4 cosA sinA + sin2A) + (cos2A - 2sinA cosA + sin2A) - 2 (2cos2A + sin2A - 3 sinAcosA) =
= (8cos2A + cos2A - 4cos2A) + (2sin2A + sin2A - 2sin2A) + (-8sinA cosA - 2sinA cosA + 6sinA cosA) =
=5 cos2A + sin2A - 4sinA cosA = ( sin2A + cos2A) + 4cosA (cosA - sinA) = 1 +

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