高分求用微积分详解一道题:设函数fn(θ)=sinθ+(-1)ncosθ,0≤θ≤π/4,其中n为正整数.⑴判断函数f1(θ)、f3(θ)的单调性,并就f1(θ)的情形证明你的结论;⑵证明:2f6(θ)-f4(θ)=(cos4θ-sin4θ)(cos2θ-sin2θ)
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![高分求用微积分详解一道题:设函数fn(θ)=sinθ+(-1)ncosθ,0≤θ≤π/4,其中n为正整数.⑴判断函数f1(θ)、f3(θ)的单调性,并就f1(θ)的情形证明你的结论;⑵证明:2f6(θ)-f4(θ)=(cos4θ-sin4θ)(cos2θ-sin2θ)](/uploads/image/z/8680768-16-8.jpg?t=%E9%AB%98%E5%88%86%E6%B1%82%E7%94%A8%E5%BE%AE%E7%A7%AF%E5%88%86%E8%AF%A6%E8%A7%A3%E4%B8%80%E9%81%93%E9%A2%98%3A%E8%AE%BE%E5%87%BD%E6%95%B0fn%28%CE%B8%29%3Dsin%CE%B8%2B%28-1%29ncos%CE%B8%2C0%E2%89%A4%CE%B8%E2%89%A4%CF%80%2F4%2C%E5%85%B6%E4%B8%ADn%E4%B8%BA%E6%AD%A3%E6%95%B4%E6%95%B0.%E2%91%B4%E5%88%A4%E6%96%AD%E5%87%BD%E6%95%B0f1%28%CE%B8%29%E3%80%81f3%28%CE%B8%29%E7%9A%84%E5%8D%95%E8%B0%83%E6%80%A7%2C%E5%B9%B6%E5%B0%B1f1%28%CE%B8%29%E7%9A%84%E6%83%85%E5%BD%A2%E8%AF%81%E6%98%8E%E4%BD%A0%E7%9A%84%E7%BB%93%E8%AE%BA%EF%BC%9B%E2%91%B5%E8%AF%81%E6%98%8E%EF%BC%9A2f6%28%CE%B8%29-f4%28%CE%B8%29%EF%BC%9D%28cos4%CE%B8-sin4%CE%B8%29%28cos2%CE%B8-sin2%CE%B8%29)
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