## kenneyfamily 2 years ago MAJOR HELP PLEASE!! Verify that the equation is an identity. Show all your work. (sin x + cos x)^2 - 1 = sin 2x

1. nubeer

(a+b)^2 =a^2+2ab+b^2 so (sin x + cos x)^2 - 1 sin^2x+2sinxcosx+cos^2x -1 2sinxcosx +sin^2x+cos^2x -1 i think u can do from here.

2. tamtoan

use formula \[(a+b)^{2} = a^{2} + 2ab + b^{2}\], expand that out and you will see what you need to

3. kenneyfamily

@nubeer i'm sorry i am a little lost, could you please explain further?

4. nubeer

2sinxcosx +sin^2x+cos^2x -1 have you understood how i have got this part?

5. kenneyfamily

yes with the formula right?

6. nubeer

2sinxcosx +sin^2x+cos^2x -1 what is sin^2x+cos^2x = ?

7. kenneyfamily

1?

8. nubeer

yes.. now put this 1 in the equation 2sinxcosx +sin^2x+cos^2x -1 2sinxcosx +1-1.. got it?

9. nubeer

@kenneyfamily so?

10. kenneyfamily

2sinxcosx

11. kenneyfamily

@nubeer right?

12. nubeer

yes and 2sinxcosx=sin2x (according to the identity)

13. kenneyfamily

you're awesome..thanks!!!

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