tan(π 4 X)如何化简

1.左＝tan(x/2+π/4)+tan(x/2-π/4)=tan[(x/2+π/4)+(x/2-π/4)][1-tan(x/2-π/4)tan(x/2+π/4)]=tanx[1-(-1)]=2tan

lim(x->0)tan(x+πsinx/(4x))=tan(0+π/4)=1

∫(tan²x+tan⁴x)dx=∫tan²x(1+tan²x)dx=∫tan²xsec²xdx=∫tan²xdtanx=(1/

根据高一的公式y=tan(π/2-x)=cotx值域是[-1,0)U(0,1]准对!

tanx定义域是(kπ-π/2,kπ+π/2)则kπ-π/2

tan（X/2+π/4)+tan（x/2-π/4）=(tanx/2+1)/(1-tanx/2)+(tanx/2-1)/(1+tanx/2)=[(tanx/2+1)^2-(tanx/2-1)^2]/[(

∵tanx的单调增区间为（2kπ-π2，2kπ+π2）∴函数f(x)＝tan(x+π4)的单调增区间为2kπ-π2＜x+π4＜2kπ+π2，即kπ−3π4＜x＜kπ+π4（k∈Z）故答案为（kπ−3π

tan(π/3)=tan(π/6+x+π/6-x)=[tan(π/6+x)+tan(π/6-x)]/[1-tan(π/6+x)tan(π/6-x)]√3-√3tan(π/6+x)tan(π/6-x)]

∵tan（x+87π）=tan（x+π+π7）=tan（x+π7）=t，∴sin(157π+x)+3cos(x−137π)sin(207π−x)−cos(x+227π)=sin(x+π7+2π)+3c

1)π/4

原式=2/tanx[1+tanxtan(x/2)]=2[(1/tanx)+tan(x/2)]=2[(cosx/sinx)+(sinx/2)/(cosx/2)]=2[(cosx/sinx)+2sin^(

证明：左边=[tan(x/2)+tan(π/4)]/[1-tan(x/2)tan(π/4)]+[tan(x/2)-tan(π/4)]/[1+tan(x/2)tan(π/4)]=[tan(x/2)+1]

设tan(x+π/4)=t则t属于（-∞,+∞）当t=2值域是（-∞,-2]并[2,+∞）因为y=t+1/t在（-∞,-1）并（1,+∞）上是单调递增的而tan(-π/4+kπ)=-1tan(π/4+

分子把平方展开之后整个式子化为4tan(x/2)/[1-(tan(x/2))^2]=2{tan(x/2)+tan(x/2)/[1-(tan(x/2))×(tan(x/2))]}=2tanx再问：。。=

证明：令tanx/2=ttan(x/2+45)=(t+1)/(1-t)tan(x/2-45)=(t-1)/(t+1)tan(x/2+45)+tan(x/2-45)=[(t+1)^2+(t-1)^2]/

tan(x/2+π/4)+tan(x/2-π/4)=[tan(x/2)+tan(π/4)]/[1-tan(x/2)tan(π/4)]+[tan(x/2)-tan(π/4)]/[1+tan(x/2)ta

secx+tanx=1/cosx+sinx/cosx=(1+sinx)/cosxtan(π/4+x/2)=[tanπ/4+tan(x/2)]/[1-tan(x/2)]=[1+tan(x/2)]/[1-

=（1+tanθ-1+tanθ）/(1-tan^2(θ))=2tanθ*cos^2(θ)/(cos^2(θ)-sin^2(θ))=2sinθcosθ/cos2θ=sin2θ/cos2θ=tan2θ其实

lim(x→0)[tan(π/4-x)]^(cotx)=lim(x→0){e^[cotx*ln(tan(π/4-x))]}只需要求lim(x→0)[cotx*ln(tan(π/4-x))]；lim(x