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
A-maths..............
2007-06-03 6:12 am
回答 (1)
2007-06-03 7:12 am
✔ 最佳答案
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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