Is my math book wrong? sin(180° ‒ α) · sin(180° + α) ‒ cos(180° + α) · cos(180° ‒ α)

[MathGuy123456789]

So I have this problem
sin(180° ‒ α) · sin(180° + α) ‒ cos(180° + α) · cos(180° ‒ α)

when you simplify
=sin α · (–sin α) – (–cos α) · (–cos α)

simplify it further
=–sin^2 α + cos^2 α

my book says then
=–(sin^2 α + cos^2 α)
thus
=-1

Can I really just put that in between brackets?

because when I put it into a website that solves math problems it outputs

=cos(2a)

What is the correct solution?

 

[MarkFL]

Your book is correct. You made a sign error, taking 3 negatives to be positive when you stated simplify further.

 

[Dr.Peterson]

So I have this problem
sin(180° ‒ α) · sin(180° + α) ‒ cos(180° + α) · cos(180° ‒ α)
...
because when I put it into a website that solves math problems it outputs

=cos(2a)

What is the correct solution?

Please show how you entered the expression into the website. An image will help.