如果(1+ sin^4θ)sinθ>(1+ cos^4θ) cosθ,且θ大于0度小于360度,求θ的范围注:那个是4次方
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如果(1+ sin^4θ)sinθ>(1+ cos^4θ) cosθ,且θ大于0度小于360度,求θ的范围注:那个是4次方
如果(1+ sin^4θ)sinθ>(1+ cos^4θ) cosθ,且θ大于0度小于360度,求θ的范围
注:那个是4次方
如果(1+ sin^4θ)sinθ>(1+ cos^4θ) cosθ,且θ大于0度小于360度,求θ的范围注:那个是4次方
(1+ sin^4θ)sinθ>(1+ cos^4θ) cosθ即sinθ+sin^5θ-cos^5θ-cosθ>0,也就是(sinθ-cosθ)+(sinθ-cosθ)(sin^4θ+sin^3θcosθ+sin^2θcos^2θ+sinθcos^3θ+cos^4θ)=(sinθ-cosθ)(1+sin^4θ+cos^4θ+sin^2θcos^2θ+sinθcosθ)=(sinθ-cosθ)(2+sinθcosθ-sin^2θcos^2θ)>0
对任意θ,(2+sinθcosθ-sin^2θcos^2θ)>0都成立,故只需sinθ-cosθ>0,而sinθ-cosθ=根号2分之一乘以sin(θ-pi/4),故θ属于(pi/4,5pi/4).
Pi/4<θ<5*Pi/4
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