已知tan(π+α)=1/3,求cos²(π+α)+sin(π+α)cos(π-α)-2cos²(3/2π-α)的值
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已知tan(π+α)=1/3,求cos²(π+α)+sin(π+α)cos(π-α)-2cos²(3/2π-α)的值
已知tan(π+α)=1/3,求cos²(π+α)+sin(π+α)cos(π-α)-2cos²(3/2π-α)的值
已知tan(π+α)=1/3,求cos²(π+α)+sin(π+α)cos(π-α)-2cos²(3/2π-α)的值
化简原式=cos²α+sinαcosα-2sin²α=(cos²α+sinαcosα-2sin²α)/(sin²α+cos²α)
=(1+tanα-2tan²α)/(tan²α+1)
tan(π+α)=tanα=1/3代入上式得:(1+1/3-2/9)/(1/9+1)=1
tan(π+α)=1/3
tanα=1/3
cos²(π+α)+sin(π+α)cos(π-α)-2cos²(3/2π-α)
=(-cosα)²+(-sinα)(-cosα)-2(-sinα)²
=cos²α+sinαcosα-2sin²α
=(cos²α+sinαcosα-2sin...
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tan(π+α)=1/3
tanα=1/3
cos²(π+α)+sin(π+α)cos(π-α)-2cos²(3/2π-α)
=(-cosα)²+(-sinα)(-cosα)-2(-sinα)²
=cos²α+sinαcosα-2sin²α
=(cos²α+sinαcosα-2sin²α)/1
=(cos²α+sinαcosα-2sin²α)/(cos²α+sin²α)分子分母同时除以cos²α
=(cos²α/cos²α+sinαcosα/cos²α-2sin²α/cos²α)/(cos²α/cos²α+sin²α/cos²α)
=(1+tanα-2tan²α)/(1+tan²α)
=[1+1/3-2*(1/3)²]/[1+(1/3)²]
=(10/9)/(10/9)
=1
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