数f(x)=cos(-x/2)+cos((4k+1/2)*派-x/2),k属于Zx属于R求f(x)周期解析式及f(x)在[0,派]上的减区间若f(a)=2√10/5,a属于(0,派/2),求tan(2a+派/4)的值

Question

数f(x)=cos(-x/2)+cos((4k+1/2)*派-x/2),k属于Zx属于R
求f(x)周期
解析式及f(x)在[0,派]上的减区间
若f(a)=2√10/5,a属于(0,派/2),求tan(2a+派/4)的值

Answer 1

f(x)=cos(-x/2)+cos[(4k+1/2)π-x/2] (注：k∈Z) =cos(x/2) +cos(π/2 -x/2) =cos(x/2)+sin(x/2) =√2*[√2/2 *cos(x/2)+√2/2 *sin(x/2)] =√2cos(x/2-π/4)则可知...