证明:cos^4 a-sin^4 a=cos^2 a(1-tan a)(1+ tan a)

证明sin^4a-cos^4a=sin^2a-cos^2a 证明:sin^4a+cos^4a=1-1/2sin^22a 证明 sin^4a+cos^4a=1-2sin^2a乘以cos^2a sinA+sinB-sinC=4sin(A/2)sin(B/2)cos(C/2)证明上式 证明cos^4 a-sin^4 a=cos^2(1-tana)(1+tana) 证明sin^4 a+cos^4 a=cos^2(1-tana)(1+tana) 证明cosA＋cosB＋cosC=1+4sin(A/2)sin(B/2)sin(C/2)证明：cosA＋cosB＋cosC=1+4sin(A/2)sin(B/2)sin(C/2)尽量详细一点选做cosA+cosB+cosC=1+4sin(A/2)sin(B/2)sin(C/2) cos(180-B-C)+cosB+cosC=1+2sin(A/2)[2sin(B/2)sin(C/2)] cos(180-B-C)+cosB+cosC 1.证明4((cos a)^6+(sin a)^6)=1+3(cos 2a)^22.证明(cos a)^6-(sin a)^6=cos 2a * (1-1/4 (sin 2a)^2) 证明sin(4A)sin(2A)(1-cos(2A)) cos(4A)cos(2A)(1 cos(2A))=cos(2A)(1 cos(6A))应该是sin4Asin2A(1-cos2A) + cos4Acos2A(1+cos2A)=cos2A(1+cos6A) 证明:cos^4 a-sin^4 a=cos^2 a(1-tan a)(1+ tan a) 证明SIN的4次方A-COS的4次方A=SIN的2次方-COS的2次方 证明 sin^4a-cos^4a=1-2cos^2asin^4a-cos^4a=1-2cos^2a 证明sin a + cos a∈[-√2,√2]顺便说明一下：为什么sin a + cos a=√2sin(α+π/4？ sin^4+sin^2cos^2+cos^2a= 若sin^4a/sin^2b+cos^4a/cos^2b=1,证明sin^4b/sin^2a+cos^4b/cos^2a=1.(不用向量怎么证?) 证明Cos^A-Sin^A=1-2Sin^A=2Cos^A-1=cos^a-sin^a 利用三角函数定义证明cos a-sin a+1/(cos a+sin a+1)=1-sin a/cos a cos^2A - cos^2B + sin^2C=2cosA *sinB *sinC证明