【高一数学】同角三角函数的化简求值》》》》已知(tanx)/(tanx-1)=-1求下列各式的值:(1)(sinx-3cosx)/(sinx+cosx)(2)(sin^2)x+sinxcosx+2
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![【高一数学】同角三角函数的化简求值》》》》已知(tanx)/(tanx-1)=-1求下列各式的值:(1)(sinx-3cosx)/(sinx+cosx)(2)(sin^2)x+sinxcosx+2](/uploads/image/z/2761451-35-1.jpg?t=%E3%80%90%E9%AB%98%E4%B8%80%E6%95%B0%E5%AD%A6%E3%80%91%E5%90%8C%E8%A7%92%E4%B8%89%E8%A7%92%E5%87%BD%E6%95%B0%E7%9A%84%E5%8C%96%E7%AE%80%E6%B1%82%E5%80%BC%E3%80%8B%E3%80%8B%E3%80%8B%E3%80%8B%E5%B7%B2%E7%9F%A5%28tanx%29%2F%28tanx-1%29%3D-1%E6%B1%82%E4%B8%8B%E5%88%97%E5%90%84%E5%BC%8F%E7%9A%84%E5%80%BC%EF%BC%9A%EF%BC%881%EF%BC%89%28sinx-3cosx%29%2F%28sinx%2Bcosx%29%EF%BC%882%EF%BC%89%28sin%5E2%29x%2Bsinxcosx%2B2)
【高一数学】同角三角函数的化简求值》》》》已知(tanx)/(tanx-1)=-1求下列各式的值:(1)(sinx-3cosx)/(sinx+cosx)(2)(sin^2)x+sinxcosx+2
【高一数学】同角三角函数的化简求值》》》》
已知(tanx)/(tanx-1)=-1求下列各式的值:
(1)(sinx-3cosx)/(sinx+cosx)
(2)(sin^2)x+sinxcosx+2
【高一数学】同角三角函数的化简求值》》》》已知(tanx)/(tanx-1)=-1求下列各式的值:(1)(sinx-3cosx)/(sinx+cosx)(2)(sin^2)x+sinxcosx+2
(tanx)/(tanx-1)=-1
tanx=1-tanx
tanx=1/2
sinx/cosx=tanx=1/2
cosx=2sin
所以(sinx-3cosx)/(sinx+cosx)
=(sinx-6sinx)/(sinx+2sinx)
=-5sinx/3sinx
=-5/3
cosx=2sinx
(sinx)^2+(cosx)^2=1
所以(sinx)^2=1/5
(cosx)^2=4/5
sinx/cosx=1/2>0
所以sinxcosx>0
sinxcosx=根号(sinx)^2*(cosx)^2=2/5
所以(sinx)^2+sinxcosx+2=1/5+2/5+2=13/5
(1)(tanx)/(tanx-1)=-1
tanx=1/2
原式上下同时除cosx
=(tanx-3)/(tanx+1)=-5/3
(2)将1化为cos^2x+sin^2x
原式=(sin^2)x+sinxcosx+2sin^2x+2cos^2x
=(3sin^2x+sinxcosx+2cos^2x)/(cos^2x+sin^2x)
上下同时除以cos^2x=(2tan^2x+tanx+2)/1+tan^2x)
=13/5