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tAn x=1/2,sin²(π/4+x)=

tanx = 1/2 2sinx= cosx 2sinxcosx = (cosx)^2 sin2x = 1/(secx)^2 = 1/[( tanx)^2 +1] =1/(1+ 1/4) = 4/5 [sin(π/4+x)]^2 =[(√2/2)(sinx+cosx) ]^2 =(1/2)(1+sin2x) =(1/2)(1+ 4/5) = 9/10

tanx = 1/2 2sinx= cosx 2sinxcosx = (cosx)^2 sin2x = 1/(secx)^2 = 1/[( tanx)^2 +1] =1/(1+ 1/4) = 4/5 [sin(π/4+x)]^2 =[(√2/2)(sinx+cosx) ]^2 =(1/2)(1+sin2x) =(1/2)(1+ 4/5) = 9/10

sin(2x+1/4π)=1/根号2(sin2x+cos2x)=1/根号2(2sinxcosx+cos^2-sin^2)= 【1/根号2(2sinxcosx+cos^2-sin^2)】/(sin^2x+cos^2) 分子分母同除cos^2 得(2tanx-tan^2+1)/根号2(tan^2+1) 又tan=1/2 所以=7根号2/10

=(1/2)cos(2x)

令tan(x-π/4)=0 x-π/4=kπ x=π/4+kπ 在(0,2π) x可取,π/4,5π/4, 则,间断点,两个

因为(π/4-x)+(π/4+x)=π/2,所以tan(π/4-x)=cot(π/4+x) (2cos²x-1)/2tan(π/4-x)sin²(π/4+x) =sin2x/[2cot(π/4+x)sin²(π/4+x)] =sin2x/{[2cos(π/4+x)/sin(π/4+x)]sin²(π/4+x)} =sin2x/[2sin(π/4+x)cos(π/4+x)] =sin2x/sin(π/2...

-√6/3 根据公式:(cosx-sinx)²=1-2sinxcosx=1-1/3=2/3 所以 cosx-sinx=+-√6/3 因为 π/4

【参考答案】D [sin(π/2-x)+sin(π-x)]/[cos(-x)+sin(2π-x)]=2009 根据诱导公式,化简 (cosx+sinx)/(cosx-sinx)=2009 左边分子分母同时除以cosx: (1+tanx)/(1-tanx)=2009 ∵tan5π/4=tan(π+π/4)=1 ∴(tan5π/4+tanx)/(1-tan5π/4tanx)=2009 根据两角和...

q用α表示了。 (tan(α+π/4)=-1/2, (tanα+1)/(1-tanα)=-1/2, ∴tanα=-3 ∴cosα=-√10/10 (sin2α-2cos^2α)/sin(α-π/4)=(2sinαcosα-2cos^2α)/sin(α-π/4) =2cosα(sinα-cosα)/sin(α-π/4) =[2cosα*√2sin(α-π/4)]/sin(α-π/4) =2√2cosα=-2√5/5 如果答案对您...

(1)∵f(x)=(1+cotx)sin 2 x-2sin(x+ π 4 )sin(x- π 4 )=sin 2 x+sinxcosx+cos2x= 1-cos2x 2 + 1 2 sin2x+cos2x = 1 2 (sin2x+cos2x)+ 1 2 ∵tanα=2,∴sin2α=2sinαcosα= 2sinα?cosα sin 2 α+cos 2 α = 2tanα 1+tan 2 α = 4 5 ,cos2α= c...

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