Addition Formula AL Maths Question

https://www.quora.com/profile/Bravewarrior/p-144659738
Here is the question and its solution. Can someone please explain the 3rd line of the solution please, thank you!

Also is it because cos of 1 and cos of -1 give the same answer? Because of the way the graph is?

Basically, cos is symmetric about the y axis (reflection) so
cos(-P) = cos(P)
whereas you can imagine sin being a reflection in y then a reflection in x so
sin(-P) = -sin(P)
Theyre basic properties which you need to know. Theyre in the CAST quadrant diagram (so if P is acute, then -P is in Q4 and P is in Q1), but its often easier to understand them in terms of the curves.

Thank you!!! The CAST diagram is a bit confusing to me but yes it is easier to look at the graph 🙂

The sinusoidal curves are often "better", but worth understanding the cast diagram in terms of a right triangle with a unit hypotenuse so something like
http://mathonline.wikidot.com/cast-rule
Then in quadrant 1, theta is positive, the point is [cos(theta), sin(theta)] and its reflection in the x axis is in quadrant 4 and that would have coordinates
[cos(-theta), sin(-theta)] = [cos(theta), -sin(theta)]
as the x coordinate is the same (positive) and the y coordinate is now negative (below the x axis).