Question

高数,正弦函数导数推论,sin(x+h)-sin(x)=2cos(x+h/2)sin(h/2)怎么但这部得?

Answer 1

sin(A+B)=sinAcosB+cosAsinB (1)

sin(A-B)=sinAcosB-cosAsinB (2)

(1)-(2)

2cosAsinB = sin(A+B)- sin(A-B)

now

A+B=x+h (3)

A-B= x (4)

=>A = x+h/2

B= h/2

=>sin(x+h)-sin(x)=2cos(x+h/2)sin(h/2)