f(x)=sin(x+四分之七乘以派)+cos(x-四分之三乘以派),求f(x)最小正周期及最小值?,

Question

f(x)=sin(x+四分之七乘以派)+cos(x-四分之三乘以派),求f(x)最小正周期及最小值?,

Answer 1

f(x)=sin(x+7π/4)+cos(x-3π/4)
=sinxcos7π/4+cosxsin7π/4+cosxcos3π/4+sinxsin3π/4
=sinx√2/2-cosx√2/2-cosx√2/2+sinx√2/2
=√2(sinx-cosx)
=2sin(x-π/4)
T=2π/1=2π,
fmin(x)=-2