1.化简:sin(4k-1/4π -a)+cos(4k+1/4π -a)(k∈Z)
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1.化简:sin(4k-1/4π -a)+cos(4k+1/4π -a)(k∈Z)
![1.化简:sin(4k-1/4π -a)+cos(4k+1/4π -a)(k∈Z)](/uploads/image/z/16707104-8-4.jpg?t=1.%E5%8C%96%E7%AE%80%3Asin%284k-1%2F4%CF%80+-a%29%2Bcos%284k%2B1%2F4%CF%80+-a%29%28k%E2%88%88Z%29)
原式=sin(kπ-π/4-a)+cos(kπ+π/4-a)
k是偶数
则原式=sin(-a-π/4)+cos(π/4-a)
=-sinacosπ/4-cosasinπ/4+cosπ/4cosa+sinπ/4sina
=0
k是奇数
则原式=sin(a-π/4)+cos(π/4+a)
=sinacosπ/4-cosasinπ/4+cosπ/4cosa-sinπ/4sina
=0
所以原式=0
k是偶数
则原式=sin(-a-π/4)+cos(π/4-a)
=-sinacosπ/4-cosasinπ/4+cosπ/4cosa+sinπ/4sina
=0
k是奇数
则原式=sin(a-π/4)+cos(π/4+a)
=sinacosπ/4-cosasinπ/4+cosπ/4cosa-sinπ/4sina
=0
所以原式=0
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