Prove that? 2√3sin(y-60)=√3siny-3cosy

1 Answer
Apr 10, 2018

See below.

Explanation:

Identity:

#color(red)bb(sin(A-B)=sinAcosB-cosAsinB)#

#LHS#

#2sqrt(3)sin(y-60)=2sqrt(3)[sin(y)cos(60)-cos(y)sin(60)]#

#sin(60)=sqrt(3)/2#

#cos(60)=1/2#

Substituting:

#2sqrt(3)sin(y-60)=2sqrt(3)[sin(y)(1/2)-cos(y)sqrt(3)/2]#

Expand:

#2sqrt(3)sin(y-60)=sqrt(3)sin(y)-3cos(y)#

#LHS -= RHS#