Can you prove the following two difficult trigonometric identities?

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SUMMARY

The discussion focuses on proving two challenging trigonometric identities: [sec(x)]^6 - [tan(x)]^6 = 1 + 3*[tan(x)]^2*[sec(x)]^2 and [sin(x)]^2*tan(x) + [cos(x)]^2*cot(x) + 2*sin(x)*cos(x) = tan(x) + cot(x). Participants highlighted the availability of a LaTeX compiler for formatting equations, which aids in presenting mathematical proofs clearly. The conversation emphasizes the importance of using LaTeX for complex mathematical expressions and encourages users to engage with the forum for further assistance.

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Students, educators, and math enthusiasts looking to deepen their understanding of trigonometric identities and enhance their skills in mathematical proof techniques.

DrLiangMath
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Can you prove the following?

[sec(x)]^6 - [tan(x)]^6 = 1 + 3*[tan(x)]^2*[sec(x)]^2

[sin(x)]^2*tan(x) + [cos(x)]^2*cot(x) + 2*sin(x)*cos(x) = tan(x) + cot(x)

If not, the following free math tutoring video shows you the method:

 
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@Dr. Liang: We have a LaTeX compiler here that you can use to type out the equations. If you don't know LaTeX reply to this to see how the coding works. The basics are simple and we have a Forum to show you how to do more complicated work.
[math]sec^6(x) - tan^6(x) = 1 + 3 ~tan^2(x) ~ sec^2(x)[/math]

[math]sin^2(x) ~ tan(x) + cos^2(x) ~ cot(x) + 2 ~ sin(x) ~ cos(x) = tan(x) + cot(x)[/math]

-Dan
 
Hello Dan,

Thank you so much for your kindness and help! I didn't notice a LaTeX compiler is available in the forum.

Derek
 
This is useful information
 

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