How do you derive the trigonometric sum and difference formulas for sin, cos, and tan? I.e: How do I derive something like sin(x+y)=sinxcosy+cosxsiny?
follow the steps
these are compound angle identities :
#-=#sinAcosB + cosAsinB
therefore: sin (A+A) = sin (2A)
= 2 sinAcosA(thats the double angle formula) <<<<<
it goes on for all the other compound angles..
:try them and let me know if you had any difficulty, i'll be glad to help :)
Use a diagram and some reasoning...
...The best math teacher I ever had taught me: memorize as little as possible in mathematics.
Words to live by, as I can never be 100% sure I remember these trig identities correctly. But refer to the diagram:
Angle AOE is the sum of angles x and y.
Furthermore, segment OA has length 1.
Note now that triangles AFD and OFB are similar.
Angle CAD is therefore x
...but we previously deduced that
Now, note that segment
And you can see from the diagram that
Segments DE and CB are equal.