- #1
thomas49th
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im stuck on the top question on part B
i can do the difference of 2 squares on the LHS but how do i get rid of the cosec²x - cot²x ??
Thanks
Solve Hard C3 Question: Get Rid of cosec²x - cot²x
- Thread starter thomas49th
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Thanks!In summary, the conversation is about finding the value of cosec^4\theta - cosec^4\theta - 1 by using the result from part a). The person is confused about how to get rid of the cosec²x - cot²x in the equation. It is suggested to use the identities cosec^2\theta + cot^2\theta = -1 and -cot^4\theta = -1 + cosec^2\theta - cosec^4\theta - cosec^2\theta to solve the equation.
im stuck on the top question on part B
i can do the difference of 2 squares on the LHS but how do i get rid of the cosec²x - cot²x ??
Thanks
- #2
3lliott
- 1
- 0
mis-post, oops!
Edit: Well, as I'm here...
[itex]cosec^2\theta - cot^2\theta = 1[/itex]
[itex]cosec^2\theta + cot^2\theta = -1[/itex]
Well, that's the RHS...
[itex]-cot^4\theta = -cot^2\theta \times cot^2\theta\newline[/itex]
[itex]= (1 - cosec^2\theta)(cosec^2\theta - 1)\newline[/itex]
[itex]= -1 + cosec^2\theta - cosec^4\theta - cosec^2\theta\newline[/itex]Back to the original question!
[itex]cosec^4\theta - cosec^4\theta - 1 = - 1\newline[/itex]
[itex]-1 = -1[/itex]I think that's correct :S
(Hmm, latex is messed up, how do I make a newline?)
Edit: Well, as I'm here...
[itex]cosec^2\theta - cot^2\theta = 1[/itex]
[itex]cosec^2\theta + cot^2\theta = -1[/itex]
Well, that's the RHS...
[itex]-cot^4\theta = -cot^2\theta \times cot^2\theta\newline[/itex]
[itex]= (1 - cosec^2\theta)(cosec^2\theta - 1)\newline[/itex]
[itex]= -1 + cosec^2\theta - cosec^4\theta - cosec^2\theta\newline[/itex]Back to the original question!
[itex]cosec^4\theta - cosec^4\theta - 1 = - 1\newline[/itex]
[itex]-1 = -1[/itex]I think that's correct :S
(Hmm, latex is messed up, how do I make a newline?)
Last edited:
- #3
Gib Z
Homework Helper
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Use the result in part a) like it told you to.
- #4
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3lliot, please do not give out answers. We offer free help here at PF, not free answers.
FAQ: Solve Hard C3 Question: Get Rid of cosec²x - cot²x
How do I simplify cosec²x - cot²x?
To simplify this expression, we can use the trigonometric identity: cosec²x = 1 + cot²x. Therefore, cosec²x - cot²x = 1 + cot²x - cot²x = 1.
Can I use a calculator to solve this hard C3 question?
Yes, you can use a calculator to solve this question. However, it is important to understand the concept of trigonometric identities and how to apply them to simplify the expression.
What is the purpose of solving this hard C3 question?
The purpose of solving this question is to strengthen your understanding of trigonometric identities and improve your problem-solving skills in mathematics.
Is there a specific method to solve this type of problem?
Yes, there are specific methods to solve this type of problem using trigonometric identities. It is important to practice and familiarize yourself with these identities to effectively solve these types of questions.
Can I use a different trigonometric identity to solve this question?
Yes, you can use different trigonometric identities to solve this question. However, it is important to choose the most appropriate identity that simplifies the expression and leads to the correct answer.