cosx=cos(π/4＋x-π/4)
=cosπ/4cos(x-π/4)-sinπ/4sin(x-π/4)
=√2/2 [cos(x-π/4)-sin(x-π/4)]
=√2/2× 【1-(x-π/4)^2/2!+(x-π/4)^4/4!-.-[(x-π/4)-(x-π/4)^3/3!+(x-π/4)^5/5!+.]】
x∈R
将cosx在x=π/4处展开成幂级数,求详解.
cosx=cos(π/4＋x-π/4)
=cosπ/4cos(x-π/4)-sinπ/4sin(x-π/4)
=√2/2 [cos(x-π/4)-sin(x-π/4)]
=√2/2× 【1-(x-π/4)^2/2!+(x-π/4)^4/4!-.-[(x-π/4)-(x-π/4)^3/3!+(x-π/4)^5/5!+.]】
x∈R