香港必買2017

標題:

A-maths..............

發問:

Show that sin(A+B)sin(A-B)=(sinA)^2-(sinB)^2.Hence (a)find all the angles between 0度and 180度 inclusive which satisfy the equation(sin3x)^2=(sinx)^2 (b)show that sin15sin75=1/4

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sin(A+B)sin(A-B) = (sinAcosB + cosAsinB)(sinAcosB - cosAsinB) = sin^2 Acos^2 B - cos^2 Asin^2 B = sin^2 A (1 - sin^2 B) - (1 - sin^2 A)sin^2 B = sin^2 A - sin^2 B a) A = 3x, B = x sin^2 (3x) - sin^2 x = sin(4x) sin(2x) = 0 sin(4x) = 0 or sin(2x) = 0 4x = 0, 180, 360, 540, 720 or 2x = 0, 180, 360 x = 0, 45, 90, 135, 180 b) A+B = 75 A-B = 15 A = 45, B = 30 sin15sin75 = sin^2 (45) - sin^2 (30) = 1/2 - 1/4 = 1/4 finished

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