化简：cot（θ+4π）*cos（θ+π）*sin（θ+3π）/tan（π+θ）*cos^3(-π-θ）求值：√1-2sin10°cos10°/cos10°-√1-cos^2170°求证：1-2sin2x*cos2x/cos^22x-sin^22x=1-tan2x/1+tan2x

Question

化简：cot（θ+4π）*cos（θ+π）*sin（θ+3π）/tan（π+θ）*cos^3(-π-θ）
求值：√1-2sin10°cos10°/cos10°-√1-cos^2 170°
求证：1-2sin2x*cos2x/cos^2 2x-sin^2 2x=1-tan2x/1+tan2x

Answer 1

cot（θ+4π）*cos（θ+π）*sin（θ+3π）/tan（π+θ）*cos^3(-π-θ）=cotθ(-cosθ)(-sinθ)/tanθcos^3θ=cos^2θ/sinθcos^2θ=1/sinθ=cscθ
√1-2sin10°cos10°/cos10°-√1-cos^2 170°=√sin^2 10°+cos^2 10°-2sin10°cos10°/cos10°-√sin^2 170°+cos^2 170°-cos^2 170°=√(sin10°-cos10°)^2/cos10°-√sin^2 170°=cos10°-sin10°/cos10°-sin170°=cos10°-sin10°/cos10°-sin10°=1
1-2sin2x*cos2x/cos^2 2x-sin^2 2x=cos^2 2x-2sin2xcos2x+sin^2 2x/cos^2 2x-sin^2 2x=1-2tan2x+tan^2 2x/1-tan^2 2x=(1-tan2x)^2/(1-tan2x)(1+tan2x)=1-tan2x/1+tan2x