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anonymous

  • 5 years ago

How do you simplifiy the expression: (1+ cot theta)(1-cot theta) - csc^2 theta ?

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  1. anonymous
    • 5 years ago
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    could give clear eqautin

  2. mathteacher1729
    • 5 years ago
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    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. :)

  3. anonymous
    • 5 years ago
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    what math teacher said. nice

  4. anonymous
    • 5 years ago
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    u reduce it further by simplifying csc and cot..?

  5. anonymous
    • 5 years ago
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    i completely understand the first part! thanks!

  6. anonymous
    • 5 years ago
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    I'm just saying..its not an equation. it needs to be simplified to an expression

  7. anonymous
    • 5 years ago
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    rewrite everything (after last step) in terms of sine and cosine and it will be easier

  8. anonymous
    • 5 years ago
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    okay I will. thanks!

  9. anonymous
    • 5 years ago
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    so the answer is (1 - cot^2 theta) - csc theta right?

  10. anonymous
    • 5 years ago
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    nevermind. 2cot^2 theta right?

  11. anonymous
    • 5 years ago
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    well i guess there are many ways to write this. i got

  12. anonymous
    • 5 years ago
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    we start with \[-cot^2(\theta)-csc^2(\theta)\]

  13. anonymous
    • 5 years ago
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    wait can I guess. thank you btw! i really appreciate your help. -2cot^2 theta

  14. anonymous
    • 5 years ago
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    hold on i forgot the original question

  15. anonymous
    • 5 years ago
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    yes! that is what i got after confusing myself. good work

  16. anonymous
    • 5 years ago
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    ahhh thank you so much!!!!!

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