Question

True or False:
sinxcosy = 1/2 (sin(x+y) + cos(x-y))

Answer 1

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.