sin2x+cos2x=根号2sin(2x+四分之派)怎么求的

问题描述:

sin2x+cos2x=根号2sin(2x+四分之派)怎么求的

sin2x+cos2x(同乘根2和根2/2)
=根2(sin2x*根2/2+cos2x*根2/2) (用根2/2=sinπ/4=cosπ/4)
=根2(sin2x*cosπ/4+cos2x*sinπ/4)
=根2(sin(2x+π/4)

sin2x+cos2x
=√2(√2/2·sin2x+√2/2·cos2x)
=√2(sin2xcosπ/4+cos2xsinπ/4)
=√2sin(2x+π/4)