Show that cos2x + cos4x + cos6x = cos4x(1+2cos2x).
hence prove the identity (sin3xcos4x)/(cos2x+cos4x+cos6x) = sinx.
Trigonometry - compound angles
2008-03-09 7:08 pm
回答 (1)
2008-03-09 7:40 pm
✔ 最佳答案
a) L.H.S. = cos 2x + cos 4x + cos 6x= cos 4x + 2 cos 4x cos 2x
= cos 4x ( 1 + 2 cos 4x )
= R.H.S.
b) L.H.S.= ( sin 3x cos 4x ) / ( cos 2x + cos 4x + cos 6x )
= ( sin 3x cos 4x ) / cos 4x ( 1 + 2 cos 4x )
= sin 3x / ( 1 + 2 cos 4x )
= ( 3 sin x - 4 sin3 A ) / [ 1 + 2 ( 1 - 2 sin2 x ) ]
= sin x ( 3 - 4 sin2 A ) / ( 3 - 4 sin2 A )
= sin x
= R.H.S.
參考: My Maths Knowledge
收錄日期: 2021-04-14 19:49:02
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