2sin^2σ*sin^2β+2cos^2σcos^2β=1+cos2σ*cos2β

因为cos[TT/2-(π/4-α)]=sin(TT/4+a)

tan(π-α)=-tanα
sin(α+π/2)=-cosα
cos(2π-α)=cosα
cos(-α-π)=-cosα
tan(2π-α)=--tanα
代入=-1

tan^2α-sin^2α=tan^2α*sin^2α
sin^2a=tan^2a-tan^2a*sin^2a
=tan^2a*(1-sin^2a) (sin^2a+cos^2a=1)
=tan^2a*cos^2a cosa=sina*tana
=sin^2a
sin^2=sin^2 恒成立,所以等式成立

2cos^2(x)-1=cos2x2tan(派/4 -x)*sin^2(派/4+x)=2tan(派/4 -x)*sin^2[派/2-(派/4-x)]=2tan(派/4 -x)*cos^2(派/4-x)=2[sin(派/4 -x)/cos(派/4 -x)]*cos^2(派/4-x)=2sin(派/4 -x)/cos(派/4 -x)=sin[2(派/4 -x)]=sin(派...

tan²α-sin²α
=sin²α/cos²α-sin²α
=(sin²α-sin²αcos²α)/cos²α
=sin²α(1-cos²α)/cos²α
=sin²α*sin²α/cos²α
=tan²α*sin²α

分母=2tan(π/4-x)*cos^2[π/2-(π/4+x)]
=2[sin(π/4-x)/cos(π/4-x)]*cos^2(π/4-x)
=2sin(π/4-x)cos(π/4-x)
=sin[2(π/4-x)]
=sin(π/2-2x)
=cos2x
分子=1/2[4cos^4(x)-4cos^2(x)+1]
=1/2(2cos^2x-1)^2
=1/2(cos2x)^2
所以原式=1/2(cos2x)^2/cos2x=1/2*cos2x

2cos^2a-1/[2tan(45度-a)*sin^2(45度+a)]
=2cos^2a-1/[2ctg(45度+a)*sin^2(45度+a)]
=2cos^2a-1/[2cos(45度+a)*sin(45度+a)]
=2cos^2a-1/sin(90度+2a)=2cos^2a-1/cos(2a)
=2cos^2a-sec(2a)

tan^2x-sin^2x=sin^2x/cos^2x-sin^2x=
(1/cos^2x-1)sin^2x=[(1-cos^2x)/cos^2x]sin^2x=
[sin^2x/cos^2x]sin^2x=tan^2xsin^2x

利用公式把变量的形式化简得越少越好
(sina)^2*(sinb)^2+(cosa)^2*(cosb)^2-1/2cos2a*cos2b
=(1-(cosa)^2)(1-(cosb)^2)+(cosa)^2*(cosb)^2-1/2(2(cosa)^2-1)(2(cosb)^2-1)
=1+(cosacosb)^2-(cosa)^2-(cosb)^2+(cosacosb)^2-1/2[1-2(cosa)^2-2(cosb)^2+4(cosacosb)^2]
=1+2(cosacosb)^2-(cosa)^2-(cosb)^2-1/2+(cosa)^2+(cosb)^2-2(cosacosb)^2
=1-1/2
=1/2

2ρ(1-cosθ)=5
ρ=2.5/(1-cosθ)
根据圆锥曲线的统一极坐标方程
ρ=ep/(1-ecosθ) 知 离心率e=1 是抛物线 p=2.5 说明是 焦准距为2.5的抛物线