## ChristopherW28 Group Title Verify that (1-cos^2x)(1+cos^2x)=2sin^2x-sin^4x is a trig identity 9 months ago 9 months ago

1. myininaya Group Title

By a certain Pythagorean identity we can say 1-cos^2(x)=?

2. ChristopherW28 Group Title

Sin^2x?

3. myininaya Group Title

yep! :)

4. myininaya Group Title

so this means we now have $\sin^2(x)(1+\cos^2(x))=2\sin^2(x)-\sin^4(x)$ now this is an identity we are trying to prove now we have one side in terms of sin and another side in terms of mixture of sin and cos

5. myininaya Group Title

We could use that same identity to rewrite cos^2(x)

6. myininaya Group Title

$1-\cos^2(x)=\sin^2(x) => \cos^2(x)=$

7. myininaya Group Title

that is a blank for you to fill in

8. ChristopherW28 Group Title

I'm lost

9. myininaya Group Title

Ok I want to rewrite cos^2(x) because the other side is just in terms of sin I know an identity that has cos^2(x) and sin^2(x) in it.

10. myininaya Group Title

$\cos^2(x)+\sin^2(x)=1$

11. myininaya Group Title

So cos^2(x)=?

12. ChristopherW28 Group Title

Sin^x+ 1

13. myininaya Group Title

1-sin^2(x)

14. ChristopherW28 Group Title

Sin^2x+1?

15. ChristopherW28 Group Title

I was close

16. myininaya Group Title

1-cos^2(x)=sin^2(x) 1-sin^2(x)=cos^2(x) cos^2(x)+sin^2(x)=1

17. myininaya Group Title

So we can back to what we are trying to prove and replace the cos^2(x) with 1-sin^2(x) $\sin^2(x)(1+(1-\sin^2(x))=2\sin^2(x)-\sin^4(x)$

18. myininaya Group Title

I replaced mr.cos^2(x) with mrs. (1-sin^2(x))

19. myininaya Group Title

now we don't need those parenthesis since there is a + in front of that parenthesis lets drop that extra stuff giving us: $\sin^2(x)(1+1-\sin^2(x))=2\sin^2(x)-\sin^4(x)$

20. myininaya Group Title

now 1+1=2 which I know you know (:p) so now you distribute on that left hand side

21. ChristopherW28 Group Title

I gtg I can figure out what's left. Friend me on Facebook @ Christopher McElhannon. I will need your help again :)

22. myininaya Group Title

I will be here most likely. I'm not much of a facebook user. I'm on facebook free diet right now. :p