## anonymous one year ago cot2x + csc2x = 2csc2x - 1 my answer > cot^2+csc^4*x^3

1. anonymous

Teacher:You cannot take terms across the = when doing a proof. You must show that the LHS=RHS. See if you can use cot^2(x)+1 = csc^2(x) to help you do this.??

2. anonymous

@freckles

3. freckles

so those things in your problem are not double angles right?

4. anonymous

idont thinks so no there not

5. xapproachesinfinity

looks like square not double angle that way the left hand side is correct

6. anonymous

yes

7. freckles

so the problem is: $\cot^2(x)+\csc^2(x)=2\csc^2(x)-1$

8. anonymous

yes

9. xapproachesinfinity

this problem wants you to use the id 1+cot^2=csc^2

10. freckles

well let's play with this: $\cot^2(x)+1=\csc^2(x)$ subtract 1 on both sides

11. freckles

this will isolate the cot^2(x) term

12. freckles

in then you will be able to write left hand side in terms of csc

13. anonymous

umm okkk

14. freckles

do this one step: subtract 1 on both sides of cot^2(x)+1=csc^2(x)

15. anonymous

cot^2(x)csc^2 right

16. freckles

what happen to the equation

17. freckles

if I asked you to subtract 1 on both sides of x+1=y what would you get after just doing that one step

18. anonymous

you would get x=y

19. freckles

i'm asking you to subtract one on both sides not one side remember whatever you do to one side of the equation you have to do to the other

20. freckles

x+1=y subtract 1 on both sides (x+1)-1=y-1 x+1-1=y-1 x=y-1

21. anonymous

ohh ok

22. freckles

$\cot^2(x)+1=\csc^2(x) \\ \text{ subtract 1 on both sides here }$

23. anonymous

cot^2(X)=CSC^2(X)-1

24. freckles

right $\cot^2(x)+\csc^2(x) \text{ was your left hand side } \\ \text{ replace} \cot^2(x) \text{ with } \csc^2(x)-1$

25. freckles

$(\csc^2(x)-1)+\csc^2(x) \\ \text{ you can drop ( ) } \\ \csc^2(x)-1+\csc^2(x)$ do you think you can finish here:

26. freckles

you know how to combine like terms right?

27. anonymous

no

28. freckles

examples of combining like terms: 5+5=2(5)=10 a+a=2a x^2+x^2=2x^2 log(x)+log(x)=2log(x) sin(x)+sin(x)=2sin(x) sin^2(x)+sin^2(x)=2sin^2(x) sin^2(x)+4sin^2(x)=5sin^2(x) can you find this: csc^2(x)+csc^2(x)=?

29. freckles

or not find but simplify

30. anonymous

(2*x)*csc^2

31. freckles

what happen to csc^2 's angle part?

32. anonymous

??

33. freckles

csc^2 has no meaning csc^2(x) has meaning

34. freckles

something has to be plugged into the csc^2 function to actually have meaning csc^2 alone means nothing

35. anonymous

so (2*x)*csc^2(X)

36. freckles

so I think you meant to write 2csc^2(x) this does not mean csc^2 times x it means csc^2 of x like means x is being plugged into the csc^2( ) function

37. freckles

where does the extra x come from

38. freckles

$\csc^2(x)+\csc^2(x)=2 \csc^2(x)$

39. anonymous

ohh i see what you mena venr mind that last statment lol

40. freckles

anyways do you have any questions on this one before I take off for a bit

41. anonymous

id thnx alot

42. freckles

np