anonymous
  • anonymous
cot2x + csc2x = 2csc2x - 1 my answer > cot^2+csc^4*x^3
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • 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.??
anonymous
  • anonymous
@freckles
freckles
  • freckles
so those things in your problem are not double angles right?

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anonymous
  • anonymous
idont thinks so no there not
xapproachesinfinity
  • xapproachesinfinity
looks like square not double angle that way the left hand side is correct
anonymous
  • anonymous
yes
freckles
  • freckles
so the problem is: \[\cot^2(x)+\csc^2(x)=2\csc^2(x)-1\]
anonymous
  • anonymous
yes
xapproachesinfinity
  • xapproachesinfinity
this problem wants you to use the id 1+cot^2=csc^2
freckles
  • freckles
well let's play with this: \[\cot^2(x)+1=\csc^2(x)\] subtract 1 on both sides
freckles
  • freckles
this will isolate the cot^2(x) term
freckles
  • freckles
in then you will be able to write left hand side in terms of csc
anonymous
  • anonymous
umm okkk
freckles
  • freckles
do this one step: subtract 1 on both sides of cot^2(x)+1=csc^2(x)
anonymous
  • anonymous
cot^2(x)csc^2 right
freckles
  • freckles
what happen to the equation
freckles
  • 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
anonymous
  • anonymous
you would get x=y
freckles
  • 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
freckles
  • freckles
x+1=y subtract 1 on both sides (x+1)-1=y-1 x+1-1=y-1 x=y-1
anonymous
  • anonymous
ohh ok
freckles
  • freckles
\[\cot^2(x)+1=\csc^2(x) \\ \text{ subtract 1 on both sides here }\]
anonymous
  • anonymous
cot^2(X)=CSC^2(X)-1
freckles
  • freckles
right \[\cot^2(x)+\csc^2(x) \text{ was your left hand side } \\ \text{ replace} \cot^2(x) \text{ with } \csc^2(x)-1\]
freckles
  • 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:
freckles
  • freckles
you know how to combine like terms right?
anonymous
  • anonymous
no
freckles
  • 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)=?
freckles
  • freckles
or not find but simplify
anonymous
  • anonymous
(2*x)*csc^2
freckles
  • freckles
what happen to csc^2 's angle part?
anonymous
  • anonymous
??
freckles
  • freckles
csc^2 has no meaning csc^2(x) has meaning
freckles
  • freckles
something has to be plugged into the csc^2 function to actually have meaning csc^2 alone means nothing
anonymous
  • anonymous
so (2*x)*csc^2(X)
freckles
  • 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
freckles
  • freckles
where does the extra x come from
freckles
  • freckles
\[\csc^2(x)+\csc^2(x)=2 \csc^2(x) \]
anonymous
  • anonymous
ohh i see what you mena venr mind that last statment lol
freckles
  • freckles
anyways do you have any questions on this one before I take off for a bit
anonymous
  • anonymous
id thnx alot
freckles
  • freckles
np

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