cos8θ-sin8θ=?

cos8θ-sin8θ=?
cos8θ-sin8θ=?

cos8θ-sin8θ=?
左边=(sinθ)^8+(cosθ)^8+2(sinθcosθ)^4-2(sinθcosθ)^4
=[(sinθ)^4-(cosθ)^4]^2+2(sinθcosθ)^4
=[(sin^2θ+cos^2θ)(sin^2θ-cos^2θ)]^2+2(sinθcosθ)^4
=[(sinθ)^2-(cosθ)^2]^2+2(sinθ)^4(cosθ)^4
=(sinθ)^4+(cosθ)^4-2(sinθ)^2(cosθ)^2+2(sinθ)^4(cosθ)^4
=[(sinθ)^2+(cosθ)^2]^2-4(sinθ)^2(cosθ)^2+2(sinθ)^4(cosθ)^4
=1-4(sinθ)^2(cosθ)^2+2(sinθ)^4(cosθ)^4