f(x)sin^4x+cos^4x-1/sin(3π/2+x)cos(3π/2-x)的奇偶性
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/06/23 22:29:44
f(x)sin^4x+cos^4x-1/sin(3π/2+x)cos(3π/2-x)的奇偶性
![f(x)sin^4x+cos^4x-1/sin(3π/2+x)cos(3π/2-x)的奇偶性](/uploads/image/z/2333175-15-5.jpg?t=f%28x%29sin%5E4x%2Bcos%5E4x-1%2Fsin%283%CF%80%2F2%2Bx%29cos%283%CF%80%2F2-x%29%E7%9A%84%E5%A5%87%E5%81%B6%E6%80%A7)
sin^4x+cos^4x-1/sin(3π/2+x)cos(3π/2-x)=sin^4x+(1-sin^2x)^2-1/sinxcosx
=-2sin^2xcos^2x/sinxcosx=-2sinxcosx=-sin2x
所以f(x)sin^4x+cos^4x-1/sin(3π/2+x)cos(3π/2-x)为奇函数
=-2sin^2xcos^2x/sinxcosx=-2sinxcosx=-sin2x
所以f(x)sin^4x+cos^4x-1/sin(3π/2+x)cos(3π/2-x)为奇函数
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