- #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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SUMMARY
The discussion centers on solving the trigonometric identity involving cosecant and cotangent functions, specifically the expression cosec²θ - cot²θ. The key conclusion is that cosec²θ - cot²θ simplifies to 1, while cosec²θ + cot²θ equals -1. The user successfully applies the difference of squares method and confirms that the original equation simplifies correctly to -1 = -1, validating their approach. The discussion emphasizes the importance of utilizing previously established results in problem-solving.
PREREQUISITES- Understanding of trigonometric identities, specifically cosecant and cotangent functions.
- Familiarity with algebraic manipulation techniques, including the difference of squares.
- Basic knowledge of LaTeX formatting for mathematical expressions.
- Experience with solving trigonometric equations and identities.
- Study the derivation and applications of trigonometric identities, focusing on cosecant and cotangent.
- Learn advanced algebraic techniques for simplifying complex trigonometric expressions.
- Explore the use of LaTeX for formatting mathematical equations in online discussions.
- Practice solving similar trigonometric problems to reinforce understanding of identities.
Students and educators in mathematics, particularly those studying trigonometry, as well as anyone seeking to enhance their problem-solving skills in algebraic manipulation of trigonometric identities.
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...
cosec^2\theta - cot^2\theta = 1
cosec^2\theta + cot^2\theta = -1
Well, that's the RHS...
-cot^4\theta = -cot^2\theta \times cot^2\theta\newline
= (1 - cosec^2\theta)(cosec^2\theta - 1)\newline
= -1 + cosec^2\theta - cosec^4\theta - cosec^2\theta\newlineBack to the original question!
cosec^4\theta - cosec^4\theta - 1 = - 1\newline
-1 = -1I think that's correct :S
(Hmm, latex is messed up, how do I make a newline?)
Edit: Well, as I'm here...
cosec^2\theta - cot^2\theta = 1
cosec^2\theta + cot^2\theta = -1
Well, that's the RHS...
-cot^4\theta = -cot^2\theta \times cot^2\theta\newline
= (1 - cosec^2\theta)(cosec^2\theta - 1)\newline
= -1 + cosec^2\theta - cosec^4\theta - cosec^2\theta\newlineBack to the original question!
cosec^4\theta - cosec^4\theta - 1 = - 1\newline
-1 = -1I 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.
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