Express sin^2 u * cos^2 u in terms of cos4u
2006-12-06 12:22:57 · 3 answers · asked by ? 3 in Science & Mathematics ➔ Mathematics
i still don't get it
2006-12-06 12:35:41 · update #1
i still don't get it!
sin^2(u)cos^2(u) in terms of cos(4u)
2006-12-06 12:37:50 · update #2
ok i think i got it now
2006-12-06 12:38:28 · update #3
sin'2 u.cos'2 u
=1/4 (2sinu cosu)'2
=1/4 (sin 2u)'2
=1/4 (1 - (cos 2u)'2)
=1/4 (1- (cos4u+1)/2)
=1/8 (1 - cos 4u)
because:
cos4u=cos2u'2-sin2u'2
=2 cos2u'2-1
hope it helps you!!
2006-12-06 12:30:07 · answer #1 · answered by Larallia 2 · 0⤊ 0⤋
By cos4u, I think you mean cos^4(u).
sin^2(u) * cos^2(u)
First, remember the trig identities. "sine squared u is equal to one minus cos squared u"
(1 - cos^2(u)) (cos^2(u)) = cos^2(u) - cos^4(u)
2006-12-06 20:29:24 · answer #2 · answered by Puggy 7 · 1⤊ 0⤋
Thats so easy I won't even give you the answer.
2006-12-06 20:30:31 · answer #3 · answered by lawmarbefree 2 · 1⤊ 1⤋