已知函数f(x=sinx+cosx)²+cos2x,求f(π/4)的值和f(x)的递增区间
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![已知函数f(x=sinx+cosx)²+cos2x,求f(π/4)的值和f(x)的递增区间](/uploads/image/z/8709735-39-5.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%9Dsinx%EF%BC%8Bcosx%EF%BC%89%26%23178%3B%EF%BC%8Bcos2x%2C%E6%B1%82f%EF%BC%88%CF%80%2F4%EF%BC%89%E7%9A%84%E5%80%BC%E5%92%8Cf%EF%BC%88x%EF%BC%89%E7%9A%84%E9%80%92%E5%A2%9E%E5%8C%BA%E9%97%B4)
已知函数f(x=sinx+cosx)²+cos2x,求f(π/4)的值和f(x)的递增区间
已知函数f(x=sinx+cosx)²+cos2x,求f(π/4)的值和f(x)的递增区间
已知函数f(x=sinx+cosx)²+cos2x,求f(π/4)的值和f(x)的递增区间
f(x)=(sinx+cosx)²+cos2x
=sin²x+cos²x+2sinxcosx+cos2x
=1+sin2x+cos2x
=1+√2sin(2x+π/4)
f(π/4)=1+1+0=2
f(x)的递增区间
2Kπ-π/2≤2x+π/4≤2K+π/2 ,K∈Z
Kπ-3π/8≤x≤Kπ+π/8 ,K∈Z