1 (sinx cosx)^2的不定积分

y=√2/2*sin2x+(1+cos2x)/2-1/2=√2/2*sin2x+1/2*cos2x=√3/2*sin(2x+z)其中tanz=(1/2)/(√2/2)=√2/2所以T=2π/2=π

y=√3sin2x-cos2x=2sin(2x-30°)ymin=-2

f(x)=(1-cos2x)/2+(√3/2)sin2x+1/2=(√3/2)sin2x-(1/2)cos2x+1=sin(2x-π/6)+1（1）最小正周期T=2π/2=π（2）f(x)max=2,

f(x)=√3sinxcosx+cos?x=√3/2sin2x+(cos2x+1)/2=√3/2sin2x+1/2cos2x+1/2=sin(2x+π/6)+1/2f(x)的最小正周期为2π/2=π∵

sin^2xtanx+cos^2x/tanx+2sinxcosx-(1+cosx/sinxcosx)=sin^3x/cosx+cos^3x/sinx+2sinxcosx-(1+cosx/sinxcos

1.因为tanx>0,所以sinx和cosx同号,不妨令二者同正sinx/cosx=3,(sinx)^2+(cosx)^2=1联立,得sinx=3√10/10,cosx=√10/10,所以2sinxc

f(x)=√3/2sin2x-1/2(1-cos2x)+1/2=√3/2sin2x-1/2+1/2cos2x+1/2=√3/2sin2x+1/2cos2x=sin(2x+π/3)

2*(sinxcosx-cos平方x)+1=2sinxcosx-2cos²x+1=2sinxcosx-cos2x=sin2x-cos2x=√2sin(2x-45°)

解题思路：利用三角函数正弦的和公式sin（x+x）可得结果解题过程：解：因为sin2x=sin（x+x）=sinxcosx+cosxsinx=2sinxcosx,所以y=2sinxcosx=sin2x

y=1/2sin(2X+TT/3)-sinXcosX=cos(2x+TT/6)sin(TT/6)=1/2cos(2x+TT/6)单调递减区间是2kπ≤2x+π/6≤2kπ+πkπ-π/12≤x≤kπ+

y=1/2sin(2x+π/3)-sinxcosx=1/2(1/2sin2x+√3/2cos2x)-1/2sin2x=1/2(-1/2sin2x+√3/2cos2x)=1/2(cosπ/6cos2x-

∫dx/(sinxcosx)=∫dx/(tanx*cosx^2)=∫dtanx/tanx=ln|tanx|+C∫dx/(sinxcosx)=∫d2x/(sin2x)=∫csc2xd2x=ln|csc2

sin2x=(2tanx)/(1+tan^2x)=4/5(1)sinxcosx=1/2sin2x=2/5(2)(2sin^2x-3sinxcosx-4cos^2x)/(sinxcosx)=2tanx-

f(x)=2sinxcosx-(2cos²x-1)=sin2x-cos2x=√2sin(2x-π/4)所以值域是[-√2,√2]

首先把分母化为1=(sinx)^2+(cosx)^2所以原式就为[(sinx)^2+(cosx)^2]/[2sinxcosx+(cosx)^2],然后分子分母同除以一个(cosx)^2式子就可以化为[

(1-2sinxcosx)(1+2sinxcosx)=(sin²x+cos²x-2sinxcosx)(sin²x+cos²x+2sinxcosx)=(sinx-

sinx+cosx/sinx-cosx=2化简得sinx=3cosxsin²=9cos²x解出sin²=9/10sinxcosx=3/10sin^2x+2sinxcosx

∫1/(sinxcosx)^3dx=8∫1/(sin2x)^3dx=-4∫1/(sin2x)^4dcos2x=-4∫1/[1-（cos2x)^2]^2dcos2x设cos2x=y上式=-4∫1/[1-

y=1+2sinxcosx+sinx+cosx=sin²x+cos²x+2sinxcosx+sinx+cosx=(sinx+cosx)²+sinx+cosx=(sinx+