为什么COS2A=4sinacosa SIN2A=COSA

(1+tana+cota)/(1+tan^2a+tana)-cota/(1+tan^2a)=(1+sina/cosa+cosa/sina)/(1+sina^2/cosa^2a+sina/cosa)-c

证明:2sin(π/4+a)sin(π/4-a)=2(sinπ/4cosa+cosπ/4sina)(sinπ/4cosa-cosπ/4sina)=2*√2/2(cosa+sina)*√2/2*(cos

用两角和/差公式展开:我用45度代表的四分之派)原式=2(sin45cosa+cos45sina)(sin45cosa-cos45sina)=2(根号2/2cosa+根号2/2sina)(根号2/2c

∵cos2a=cos²a-sin²a∴原式=(sin²a+cos²a+sin2a-cos²a+sin²a)/(sin²a+cos&

原式=-(cos2a-sin2a)/[cos2a(sina+cosa)]=-cos2a/[cos2a(sina+cosa)]=-1/(sina+cosa)

cos2a=3/52(cosa)^2-1=1-2(sina)^2=3/5(cosa)^2=4/5,(sina)^2=1/5sin^4+cos^4=[(sina)^2+(cosa)^2]^2-2(sin

证明：对于任意角A,因为COSA的4次方-SINA的4次方=(COSA的2次方+SINA的2次方)*(COSA的2次方-SINA的2次方)=1*(COSA的2次方-SINA的2次方)=COS2ACOS

证明：（3-4cos2A+cos4A）/（3+4cos2A+cos4A）=(4-4cos2A+cos4A-1)/(4+4cos2A+cos4A-1)=(8sin²A-2sin²2A

cos2a=cosa^2-sina^2=1-2sina^2=2cosa^2-1

sin²a+cos²a=1sina=4/5所以cosa=±3/5sin2a=2sinacosa=±24/25cos2a=cos²a-sin²a=-7/25tan

证明：左边=2[sin(π/4)cosa+cos(π/4)sina][sin(π/4)cosa-cos(π/4)sina]=2[cosa/√2+sina/√2][cosa/√2-sina/√2]=(c

sin^4(a)-cos^4(a)=(sin^2a+cos^2a)(sin^2a-cos^2a)=-(cos^2a-sin^2a)=-cos(2a)

证明:1-cos(2A)=2*[(sinA)^2]1+cos(2A)=2*[(cosA)^2]sin(2A)=2sinA*cosA==>(1+sin2A-cos2A)/(1+sin2A+cos2A)=

tan(4分之派+a)=(tan(pi/4)+tana)/(1-tan(pi/4)tana)=(1+tana)/(1-tana)=1/2tana=-1/3(sin2a-cos2a)/(1+cos2a)

(sin²a-2sinacosa-cos²a)/(4cos²a-3sinacosa)（题目是这样吗）分子分母同时除以cos²a得原式=（tan²a-2

分子=sin²a+cos²a+2siacosa-(cos²a-sin²a)=(sina+cosa)²-(cosa+sina)(cosa-sina)=(

因为cosa=cos(2a-a)=cos2a*cosa+sin2a*sina,cos3a=cos(2a+a)=cos2a*cosa-sin2a*sina所以：cosa+cos3a=2cos2a*cos

两端平方得[sin(π/4-a)]^2=49/625,所以1-2[sin(π/4-a)]^2=527/625,即cos[2(π/4-a)]=527/625,也就是cos(π/2-2a)=527/625

sin2a=cos2a*2=2cos2acos2a=-sin2a*2=-22sin2a

sin2a=2sina*cosacos2a=cos²a-sin²a=2cos²a-1=1-2sin²a所以(1+cos2a)/sin2a-sin2a/(1-co