Best Answer

Verify 8sin^2(x)cos^2(x)=1-cos(4x)?
starfire
26-Feb-13 12:01:24 PM
0
8 * sin(x)^2 * cos(x)^2 =>
2 * 4 * sin(x)^2 * cos(x)^2 =>
2 * (2 * sin(x) * cos(x))^2 =>
2 * sin(2x)^2 =>
2 * sin(4x / 2)^2 =>
2 * (1/2) * (1 - cos(4x)) =>
1 - cos(4x)

Why?

sin(t/2) = sqrt((1/2) * (1 - cos(t)))

4  Replies

Verify 8sin^2(x)cos^2(x)=1-cos(4x)?
ray
26-Feb-13 12:01:24 PM
0
8 * sin(x)^2 * cos(x)^2 =>
2 * 4 * sin(x)^2 * cos(x)^2 =>
2 * (2 * sin(x) * cos(x))^2 =>
2 * sin(2x)^2 =>
2 * sin(4x / 2)^2 =>
2 * (1/2) * (1 - cos(4x)) =>
1 - cos(4x)

Why?

sin(t/2) = sqrt((1/2) * (1 - cos(t)))
Verify 8sin^2(x)cos^2(x)=1-cos(4x)?
sunrise
26-Feb-13 12:01:24 PM
0
8sin^2(x)cos^2(x)=1-cos(4x)

2(4sin^2(x)cos^2(x)) =
= 2(2(sin x)(cos x))^2 = ............2(sin x)(cos x) = sin 2x
= 2(sin 2x)^2 =

1 - cos(4x) = 1 - (1 - 2(sin 2x)^2) = 2(sin 2x)^2

cos 2y = (cos y)^2 - (sin y)^2 = 1 - 2(sin y)^2
Verify 8sin^2(x)cos^2(x)=1-cos(4x)?
swing
26-Feb-13 12:01:24 PM
1
8sin^2(x)cos^2(x)
=2*{2sin x cos x)^2
=2sin^2(2x)
=1-cos4x
Verify 8sin^2(x)cos^2(x)=1-cos(4x)?
sabin
26-Feb-13 12:01:24 PM
1
8sin^2(x)cos^2(x) = 8*(sin(2x)/2)^2 = 2*sin^2(2x) = (1 - cos(4x))

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