## denniel 3 years ago Prove this identity sin(2A)=2sinAcosA.

1. Tonks

Start by considering 2A as A+A ... does that make you think of any particular theorem?

2. TuringTest

...of course that makes me want to know how to prove the theorem you are thinking of @Tonks

sin(a+a)=sinacosb+cosasinb put the value of a and be here.

4. micahwood50

We know that sin(2A) = sin(A + A) sin (A + A) = cosA sinA + cosA sinA = 2 sinA cosA QED

5. Tonks

@TuringTest try stacking triangles in the unit circle... or is that for cosine?

6. TuringTest

I know it was some geometric proof like that, I don't remember those darn things...

7. micahwood50

Is that enough or do you need proof for sin (A + B) = cosA sinB + cosB sinA

8. micahwood50

formula you have given is wrong @micahwood50

10. TuringTest

it's correct

11. micahwood50

For proof of sin (A + B) = cosA sinB + cosB sinA: http://en.wikipedia.org/wiki/Proofs_of_trigonometric_identities#Sine

13. TuringTest

yep, that's the one...

14. micahwood50

15. TuringTest

perhaps you are neglecting the fact that multiplication is commutative muhammad?

16. micahwood50

|dw:1350147756505:dw|

ok i got it!! he has just rearranged the places of cos and sin.

18. TuringTest

in English that's called the commutative property of addition.

yup.

20. micahwood50

Yeah, sorry about that, though. It's easier for me to remember this formula this way.

@micahwood50 can this destroy the problem of sin(45-30) solve with your formula.

cos45*sin30-cos45sin30

23. micahwood50

Well, with minus, it's different story.

ok do sin(45+30)=cos45sin30+cos30sin45

25. micahwood50

Yeah, I got it. Thanks, though.

bro never mind if i disturb you! Accept just like the game of trig!

27. micahwood50

@muhammad9t5 I know the formulas, you don't have to correct me. Thanks, though.