...若tanx=1/2, 求sin^2x+2sinxsin(π/2-x)+3sin^2(3π/2-x)_百度知 ...

tanx=1/2，sinx/cosx=1/2→sinx=cosx/2①.sin^2x+cos^2x=1②。联立两式得:cos^2x=4/5 sin^2x+2sinxsin(π/2-x)+3sin^2(3π/2-x)=(1-cos2x)/2+2sinxcosx+3【1-cos2（3π/2-x）】/2 =1/2-cos2x/2+cos^2x+3/2+3cos2x/2 =2+cos^2x+cos2x=2+cos^2x+2cos^2x...

因为tanx=1/2 所以sinx/cosx=1/2,即2sinx=cosx 所以 原式=(sinx+6sinx)/(sinx+2sinx)=7/3 同上理，原式=3sin^2(x)+2 因为sin^2(x)+cos^2(x)=1 所以5sin^2(x)=1 所以sin^2(x)=1/5 所以 原式=3×1/5+2=13/5 ...

tanx=1/2=>2sinx=cosxsin^2x+cos^2x=1 x为锐角 sinx=√5/5 cosx=2√5/5sin2x=2sinxcosx=4/5 cos2x=3/5(sin2xcosx-sinx)/(sin2xcos2x)=(4/5*2√5/5-√5/5) /(4/5 *3/5)=3√5/25

tan2x=2tanx/[1-(tanx)^2]=1/(1-1/4)=4/3 x属于（0，π/2），2x属于（0，π）由tan2x>0知2x<π/2 则cos2x=1/√[1+(tan2x)^2]=1/√(1+16/9)=3/5 sin2x=√[1-(cos2x)^2]=4/5 sin(2x+π/3)=sin2xcos(π/3)+cos2xsin(π/3)=(4/5)*(1/2)+(3/5)*(...

(1)分子分母除以cosX (2-3tanX)/(3+4tanX)=(1/2)/(3+2)=1/10 (2)添加分母,1=(sinX)^2+(cosX)^2,分子分母除以(cosX)^2有((tanX)^2-3tanX+4)/((tanX)^2+1)=(1/4-3/2+4)/(1/4+1)=(11/4)/(5/4)=11/5

tan(π+x)=tanx=sinx/cosx=1/2 跟sinx^2+cosx^2=1联立可以解得 sinx= (根号5)/5 cosx=(2根号五)/5 或sinx=- (根号5)/5 cosx=-(2根号五)/5 sin(3/2π+X)=-cosx=(2根号五)/5 sinx（sinx-cosx）=-1/5 或 sin(3/2π+X)=-cosx=-(2根号五)/5 sinx（sinx-cosx）=-...

分子分母同时除以 cosx =(tanx-1)/(2tanx+3) tanx=1/2 代入 =(1/2-1)/(1+3)=-1/8 sinx cosx =sinx cosx/(sin^2x+cos^2x) 分子分母同时除以 cos^2x =tanx/(tan^2x+1) tanx=1/2 代入 =(1/2)/(1/4+1)=2/5 ...

tanx=sinx/cosx=1/2 cosx=2sinx (sinx)^2+(cosx)^2=5/4(cosx)^2=1 (cosx)^2=4/5 cosx=(+/-)2/5根号5 故y=2*4/5+1(+/-)2/5根号5=(13(+/-)2根号5)/5 y=2(cosx+1/4)^2+7/8 而0<=cosx<=1 故当cosx=0时有最小值是y=1,当cosx=1时有最大值是4 即值域...

解 （1）f（x）=sin2x+2sinx?cosx+3cos2x=sin2x+2sinxcosx+3cos2xsin2x+cos2x=tan2x+2tanx+3tan2x+1=175；（2）f（x）=sin2x+2sinx?cosx+3cos2x=sin2x+cos2x+2=2sin（2x+π4）+2，∵ω=2，∴f（x）的最小正周期为T=2π2=π；由π2+2kπ≤2x+π4≤3π2+2kπ，k∈Z...

cos2x=(1-tanx*tanx)/(1+tanx*tanx)=-7/25 代入得 f(x)=2+24/25-7/25=2.56 2 由1得 f(x)=2+sin2x+cos2x=2+根号2*sin（2x+π/4）由于x的范围是【0,π/2】，所以2x+π/4的范围是【π/4,5π/4】所以最大值为f(x)=f(π/4)=2+根号2 最小值为 f((x)=f(π/...