√2sin(x/2+π/4)cos(x/2)=√2/2sin(x+π/4)+ 1/2 怎么得到的
1个回答

√2sin(x/2+π/4)cos(x/2)

=√2(sin(x/2)cosπ/4+sinπ/4cos(x/2))cos(x/2)

=√2(√2/2sin(x/2)+√2/2cos(x/2))cos(x/2)

=sin(x/2)cos(x/2)+cos²(x/2)

=sin2x/2+(1+cos2x)/2

=sin2x/2+cos2x/2+1/2

=(√2/2)[sin2x(√2/2)+cos2x(√2/2)]+1/2

=(√2/2)[sin2xcosπ/4+cos2xsinπ/4]+1/2

=√2/2sin(x+π/4)+ 1/2

很高兴为您解答,skyhunter002为您答疑解惑

如果本题有什么不明白可以追问,