Add the sum and difference identities for sin x to derive 1/2 [sin(x+y)+sin(x-y)]=sin x cos y

true

Step-by-step explanation:

1/2 (sin(x+y)+sin(x-y))

= 1/2 (sin x cos Y + cos x sin y + sin x cos y - cos x sin y)

= 1/2 * 2 sin x cos y

= sin x cos y

The expression is true.

19

step-by-step explanation:

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation: