標題:
sum and product formlae
發問:
最佳解答:
Prove (sinA+sin3A+sin5A)/( cosA+cos3A+cos5A)=ta n3A sinA+sin 3A +sin 5A = sin 3A + (sin 5A +sinA) = sin 3A + {2sin[( 5A +A)/2]cos[( 5A -A)/2] = sin 3A + 2(sin 3A )(cos 2A ) = (sin 3A )(1+2cos 2A ) cosA+cos 3A +cos 5A = cos 3A + (cos 5A + cosA) = cos 3A + {2cos[( 5A +A)/2]cos[( 5A -A)/2] = cos 3A + 2(cos 3A )(cos 2A ) = (cos 3A )(1+2cos 2A ) (sinA+sin 3A +sin 5A )/(cosA+cos 3A +cos 5A )= = (sin 3A )(1+2cos 2A )/(cos 3A )(1+2cos 2A ) = sin 3A /cos 3A = tan 3A Solve cosx-cos3x=sinx-sin3 x ( 0 degree to 360 degree) 0 <= x <= 360 cosx - cos3x= sinx- sin3x (using sum to product formulae) -2sin2xsinx = 2cos2xsinx 2cos2xsinx + 2sin2xsinx = 0 sinx(cos2x + sin2x) = 0 sinx = 0 or cos2x + sin2x = 0 x = 0 or 180 or 360 or 1 + tan2x = 0 x = 0 or 180 or 360 or tan2x = -1 x = 0 or 180 or 360 or 2x = 135 or 315 or 495 or 675 x = 0 or 180 or 360 or x = 67.5 or 157.5 or 247.5 or 337.5 so x = 0 or 67.5 or 157.5 or 180 or 247.5 or 337.5 or 360
其他解答:4E350C6F8B48ECA2
sum and product formlae
發問:
此文章來自奇摩知識+如有不便請留言告知
I can't prove the following identity (sinA+sin3A+sin5A)/(cosA+cos3A+cos5A)=tan3A Also the following equation can't be solved by me cosx-cos3x=sinx-sin3x ( 0 degree to 360 degree)最佳解答:
Prove (sinA+sin3A+sin5A)/( cosA+cos3A+cos5A)=ta n3A sinA+sin 3A +sin 5A = sin 3A + (sin 5A +sinA) = sin 3A + {2sin[( 5A +A)/2]cos[( 5A -A)/2] = sin 3A + 2(sin 3A )(cos 2A ) = (sin 3A )(1+2cos 2A ) cosA+cos 3A +cos 5A = cos 3A + (cos 5A + cosA) = cos 3A + {2cos[( 5A +A)/2]cos[( 5A -A)/2] = cos 3A + 2(cos 3A )(cos 2A ) = (cos 3A )(1+2cos 2A ) (sinA+sin 3A +sin 5A )/(cosA+cos 3A +cos 5A )= = (sin 3A )(1+2cos 2A )/(cos 3A )(1+2cos 2A ) = sin 3A /cos 3A = tan 3A Solve cosx-cos3x=sinx-sin3 x ( 0 degree to 360 degree) 0 <= x <= 360 cosx - cos3x= sinx- sin3x (using sum to product formulae) -2sin2xsinx = 2cos2xsinx 2cos2xsinx + 2sin2xsinx = 0 sinx(cos2x + sin2x) = 0 sinx = 0 or cos2x + sin2x = 0 x = 0 or 180 or 360 or 1 + tan2x = 0 x = 0 or 180 or 360 or tan2x = -1 x = 0 or 180 or 360 or 2x = 135 or 315 or 495 or 675 x = 0 or 180 or 360 or x = 67.5 or 157.5 or 247.5 or 337.5 so x = 0 or 67.5 or 157.5 or 180 or 247.5 or 337.5 or 360
其他解答:4E350C6F8B48ECA2
請先 登入 以發表留言。