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log2Cos20度+log2Cos40度+log2Cos80度

log2cosπ9+log2cos2π9+log2cos4π9=log2(cosπ9?cos2π9?cos49π)=log2(sin2π92sinπ9?sin4π92sin2π9?sin8π92sin4π9)=log218=-3.

log2cos3.14/9+log2cos6.28/9+log2cos12.56/9 =log2(cos3.14/9*cos6.28/9*cos12.56/9) =log2(cos3.14/9*2*sin3.14/9cos6.28/9*cos12.56/9/2*sin3.14/9) =log2(sin6.28/9*cos6.28/9*cos12.56/9/2*sin3.14/9) =log2(2*sin6.28/9*cos6.28/9*cos12.5...

∵4cos2(xy)+14cos2(xy)≥2,∴log2[4cos2(xy)+14cos2(xy)]≥1,当且仅当4cos2(xy)=14cos2(xy),即4cos2(xy)=1时等号成立.令y=2,得lny-y2+lne22=1,∴4cos2(2x)=1,cos4x=-12,∴ycos4x=-1.故答案为:-1.

log2cosπ/5+log2cos2π/5 =log2(cosπ/5*cos2π/5) =log2[(2sinπ/5*cosπ/5*cos2π/5)/2sinπ/5] =log2[(sin2π/5*cos2π/5)/2sinπ/5] =log2[(sin4π/5)/2*2sinπ/5] =log2(1/4) =-2

∵log2m=log2cosα?log2sinα,log2n=log2cosα?log2cosαlog2p=log2sinα?log2cosα又由α∈(0,π4),得0<sinα<cosα<1,log2sinα<log2cosα<0∴log2m=log2p>log2n,∴m=p>n故选:A.

y=log2(1+cos(9/2π-a))+log2(1+sin(a-5π)) =log2[(1+cos(π/2-a))((1+sin(a-π)] =log2[(1+sina)(1-sina)] =log2(cos^2a) =2log2|cosa| a属于【0,π/4】, 根号2/2=cosa=1 -1/2=log2cosa=0 -1=2log2|cosa|=0

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∵f(x)=cosπx,∴f(x+1)=cos[π(x+1)]=-cosπx是偶函数,故①正确;∵g(x)=|log2|x-1||的定义域是{x|x≠1},∴g(x)既不是奇函数,也不是偶函数,故②错误;在同一坐标系中两函数的图象如图: 由图象可知两函数有4个不同的交点A,B,C,D,并且A...

对于A.有f(-x)=f(x),为偶函数,当x>0时,y=2-x单调递减,故A不满足;对于B.有f(-x)=f(x),为偶函数,当x>0时,y=2log2x单调递增,故B满足;对于C.y=x2+x不是偶函数,也不是奇函数,故C不满足;对于D.函数是偶函数,在(2kπ-π,2k...

(Ⅰ)x=log2(sinθ+cosθ)=log2[2sin(θ+π4)],…(2分)∵0<θ<π2,∴π4<θ+π4<3π4,…(4分)∴1<2sin(θ+π4)≤2,即0<x≤12.…(7分)(Ⅱ)设u(x)=x+1x,则u′(x)=1-1x2,…(8分)当0<x≤12时,u′(x)<0,故u(x)在(0,12]上是减函数. …...

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