Answer:
False
Step-by-step explanation:
We simplify the right hand side of the expression to check if its equal to the left hand side of the expression or not.
\(\frac{1}{2}(\sin(x+y)+\cos(x-y))\)
Use the formulas:
sin (x+ y) = sinxcosy +cosxsiny
cos (x-y)= cosxcosy +sinxsiny
Thus, the expression will become
\(\frac{1}{2}(sinxcosy+cosxsiny+cosxcosy+sinxsiny)\)
We cannot simplify this expression further.
We can see that the expression is not equal to the left hand side of the expression.
Hence, the statement is False.
