anonymous
  • anonymous
How do you simplifiy the expression: (1+ cot theta)(1-cot theta) - csc^2 theta ?
Mathematics
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anonymous
  • anonymous
How do you simplifiy the expression: (1+ cot theta)(1-cot theta) - csc^2 theta ?
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
could give clear eqautin
mathteacher1729
  • mathteacher1729
Perfect square binomial: \[(1-x)(1+x)=1-x^2\] In this case "x" = \(\cot(\theta)\). So that means \( (1+\cot (\theta))(1-\cot (\theta)) = 1 - \cot^2(\theta)\) The expression is now \(1-\cot^2(\theta) - \csc^2(\theta)\). We can use some trig identities here to reduce \(1-csc^2(\theta) = -cot^2(\theta)\) Now our final answer is almost in front of us. :)
anonymous
  • anonymous
what math teacher said. nice

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anonymous
  • anonymous
u reduce it further by simplifying csc and cot..?
anonymous
  • anonymous
i completely understand the first part! thanks!
anonymous
  • anonymous
I'm just saying..its not an equation. it needs to be simplified to an expression
anonymous
  • anonymous
rewrite everything (after last step) in terms of sine and cosine and it will be easier
anonymous
  • anonymous
okay I will. thanks!
anonymous
  • anonymous
so the answer is (1 - cot^2 theta) - csc theta right?
anonymous
  • anonymous
nevermind. 2cot^2 theta right?
anonymous
  • anonymous
well i guess there are many ways to write this. i got
anonymous
  • anonymous
we start with \[-cot^2(\theta)-csc^2(\theta)\]
anonymous
  • anonymous
wait can I guess. thank you btw! i really appreciate your help. -2cot^2 theta
anonymous
  • anonymous
hold on i forgot the original question
anonymous
  • anonymous
yes! that is what i got after confusing myself. good work
anonymous
  • anonymous
ahhh thank you so much!!!!!

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