Question

求证：(1-cos2θ-sin2θ)/(1-cos2θ+sin2θ)=tan(θ-π/4)

过程~~

谢谢

Answer 1

(1-cos2a-sin2a)/(1-cos2a+sin2a)
=[1-(1-2sin^2 a)-sin2a]/[1-(1-2sin^2 a)+sin2a]
=[2sin^2 a-sin2a]/[2sin^2 a+sin2a]
=[2sin^2 a-2sina*cosa]/[2sin^2 a+2sina*cosa]
=[2sina(sina-cosa)]/[2sina(sina+cosa)]
=(sina-cosa)/(sina+cosa)
=[根号2*sin(a-π/4)]/[根号2*sin(a+π/4)]
=sin(a-π/4)/sin(a+π/4)
=sin(a-π/4)/cos(a+π/4-π/2)
=sin(a-π/4)/cos(a-π/4)
=tan(a-π/4)