y=sinxcosx=√2(√2/2sinx+√2/2cosx)怎麼变√2sin(x+派/4)?2

1个回答

  • y=sinx+cosx

    =√2(√2/2sinx+√2/2cosx)

    =√2(sinxcos派/4+cosxsin派/4)

    =√2sin(x+派/4)

    ∵1-cos2x=2sin^2x

    ∴2(cos2x-1)^2

    =2(-2sin^2x)^2

    =8(sinx)^4

    ∵cos2x= 2cos^2x-1

    ∴y=sin2x+2cos^2x-1

    =sin2x+cos2x

    =√2(√2/2sin2x+√2/2cos2x)

    =√2(sin2xcos派/4+cos2xsin派/4)

    =√2sin(2x+派/4)

    y=sin^2+√3sinxcosx+2cosx^2

    =sin^2+cosx^2+cosx^2+√3sinxcosx

    =1+cosx^2+√3sinxcosx

    =1+1/2(1+cos2x)+√3/2sin2x

    =3/2+sin2xcos派/6+cos2xsin派/6

    =3/2+sin(2x+派/6)