Prove that: 2cosxcosy=cos(x+y)+cos(x-y)
In 2cosxcosy=cos(x+y)+cos(x-y),
Taking R.H.S. we have,
R.H.S.=cos(x+y)+cos(x-y) …..(i)
By trigonometric identities, we can write;
cos(x+y)=cosxcosy–sinxsiny
cos(x-y)=cosxcosy+sinxsiny
Therefore putting these values in eq(i), we get,
R.H.S.=(cosxcosy–sinxsiny)+(cosxcosy+sinxsiny)
=2cosxcosy
=L.H.S.
Hence, it is proved that 2cosxcosy=cos(x+y)+cos(x-y).