Question

高中数学公式推导，会的来，不废话

Answer 1

A+B+C=π，从而A+B=π-C,A/2+B/2=π/2-C/2,
由诱导公式有：sinα=sin(π-α),cosα=-cos(π-α),sin(α)=cos(π/2-α)
代入即可

Answer 2

就用Pi-C代替A+B.然后运用，sin（pi-C）=sinpi*cosC-cosPi*sinC sinC cos（pi-C）=-cosC
sin（（pi-A-B）/2）=sin

Answer 3

1
sin(A+B)=sin(π-C)=sin[π/2-(C-π/2)]=COS(C-π/2)=COS(π/2-C)=SINC

2
COS(A+B)=COS(π-C)=COS[π/2-(C-π/2)]=SIN(C-π/2)=-SIN(π/2-C)=-COSC

3
SIN[(A+B)/2]=COS[π/2-(A+B)/2]=COS[(π-A-B)/2]=COS(C/2)

Answer 4

A+B=π-C

sin(A+B)=
sin(π-C)=sinC

cos(A+B)=
cos(π-C)=-cosC

(A+B)/2=(π-C)/2=π/2-C/2

sin[(A+B)/2]=
sin(π/2-C/2)=
cos(C/2)