# 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?

##### 2 Answers

follow the steps

#### Explanation:

these are compound angle identities :

- sin(A+B)
#-=# sinAcosB + cosAsinB

from that:

put B=A

therefore: sin (A+A) = sin (2A)

= sinAcosA+cosAsinA

= 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...

#### Explanation:

...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.

Therefore,

Note now that triangles AFD and OFB are similar.

Angle CAD is therefore x

Line Segments

...but we previously deduced that

Now, note that segment

And you can see from the diagram that

Therefore segment

Segments DE and CB are equal.

Therefore, Segments

GOOD LUCK