How do you sipmify this ?

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1 Answer
Øko
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#

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