It is given that cos^2 y + cos y = p . Determine the value of p if sin y = sin y . Cos y

Are you using the . in siny.cosy as a multiplication sign?

If so, then
siny = sinycosy
cosy = 1

and cos^2 y + cosy = p
1+1 = p

p = 2

Am I missing something here??
Looks too easy, did you have a typo?

of course , if siny = 0, then we have cosy = 1 or -1.

You can try those for other solutions.

To determine the value of p, we need to use the given equation cos^2 y + cos y = p and the equation sin y = sin y . Cos y.

First, let's simplify the equation sin y = sin y . Cos y:

sin y = sin y . Cos y

Divide both sides by sin y:

1 = cos y

Now we know that cos y = 1.

Next, let's substitute this value of cos y into the first equation cos^2 y + cos y = p:

(1)^2 + 1 = p

Simplifying:

1 + 1 = p

2 = p

Therefore, the value of p is 2.