# 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 cos

= (8cos

=5 cos

cosA - sinA = y.

2x*x+y*y-2xy= 2* (2cosA - sinA)*(2cosA - sinA) + (cosA - sinA)(cosA - sinA) - 2 *(2cosA - sinA)* (cosA - sinA) =

= 2 (4 cos

^{2}A - 4 cosA sinA + sin^{2}A) + (cos^{2}A - 2sinA cosA + sin^{2}A) - 2 (2cos^{2}A + sin^{2}A - 3 sinAcosA) == (8cos

^{2}A + cos^{2}A - 4cos^{2}A) + (2sin^{2}A + sin^{2}A - 2sin^{2}A) + (-8sinA cosA - 2sinA cosA + 6sinA cosA) ==5 cos

^{2}A + sin^{2}A - 4sinA cosA = ( sin^{2}A + cos^{2}A) + 4cosA (cosA - sinA) = 1 +Need a fast expert's response?

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