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Sin2x +sin2y =1/2 , cos2x +cos2y =3/2 then the value of cos2 (x-y) is?

Sin2x +sin2y =1/2 , cos2x +cos2y =3/2 then the value of cos2 (x-y) is?

Grade:11

1 Answers

Dhruvit Raithatha
32 Points
6 years ago
\\(sin(2x) + sin(2y))^2 + (cos(2x) + cos(2y))^2 = (1/2)^2 + (3/2)^2 \\(sin^2(2x) + cos^2(2x)) + (sin^2(2y) + cos^2(2y)) + 2(sin(2x)sin(2y) + cos(2x)cos(2y)) = 10/4 \\1 + 1 + 2(sin(2x)sin(2y) + cos(2x)cos(2y)) = 10/4 \\sin(2x)sin(2y) + cos(2x)cos(2y) = 1/4 \\\\cos (2x - 2y) = cos(2x)cos(2y) + sin(2x)sin(2y) = 1/4

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