化简y=1+sinx+cosx+sinxcosx

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/30 03:01:07

化简y=1+sinx+cosx+sinxcosx
化简y=1+sinx+cosx+sinxcosx

化简y=1+sinx+cosx+sinxcosx
y=1+sinx+cosx+sinxcosx=(sinx+1)(cosx+1)

y=1/2cos x+sinxcosx+3/2sin x =1/2+sinxcosx+sin x =1/2+1/2sin2x+(1-cos2x)/2 =1/2sin2x-1/2cos2x+1 =√2/2sin(2x-π/4)+1 ..

y=1+√2(√2/2sinx+√2/2cosx)+1/2sin2x
=1+√2sin(x+π/4)+1/2sin2x