How do you sipmify this ?

pp

1 Answer
Apr 18, 2018

(sin(a+b)-cos(a)sin(b))/(sin(a-b)+cos(a)sin(b))=1

Explanation:

We want to simplify

(sin(a+b)-cos(a)sin(b))/(sin(a-b)+cos(a)sin(b))

The angle sum/difference identities

  • color(red)(sin(a+b)=sin(a)cos(b)+cos(a)sin(b)
    color(red)(=>sin(a+b)-cos(a)sin(b)=sin(a)cos(b)

  • color(blue)(sin(a-b)=sin(a)cos(b)-cos(a)sin(b)
    color(blue)(=>sin(a-b)+cos(a)sin(b)=sin(a)cos(b)

Using the identities

(sin(a+b)-cos(a)sin(b))/(sin(a-b)+cos(a)sin(b))= (sin(a)cos(b))/(sin(a)cos(b))=1