MHB Can you prove the following two difficult trigonometric identities?

AI Thread Summary
The discussion focuses on proving two challenging trigonometric identities involving secant, tangent, sine, and cosine functions. Participants are encouraged to use the available LaTeX compiler for clear expression of mathematical equations. A free math tutoring video is suggested for those needing assistance with the proof methods. The conversation highlights the importance of community support in tackling complex mathematical problems. Overall, the forum serves as a resource for learning and collaboration in mathematics.
DrLiangMath
Messages
21
Reaction score
0
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:

 
Mathematics news on Phys.org
@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
 
Thread 'Video on imaginary numbers and some queries'

Thread 'Video on imaginary numbers and some queries'

Hi, I was watching the following video. I found some points confusing. Could you please help me to understand the gaps? Thanks, in advance! Question 1: Around 4:22, the video says the following. So for those mathematicians, negative numbers didn't exist. You could subtract, that is find the difference between two positive quantities, but you couldn't have a negative answer or negative coefficients. Mathematicians were so averse to negative numbers that there was no single quadratic...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »
Thread 'Unit Circle Double Angle Derivations'

Thread 'Unit Circle Double Angle Derivations'

Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...
View full post »

Similar threads

B Trigonometric Identity involving sin()+cos()
Replies
11
Views
2K
B Can 2(sinx) be called a 'trigonometric function'?
Replies
28
Views
3K
Trigonometry Identity Question
Replies
2
Views
1K
MHB Prove (tan^2 t−1)/(sec^2 t)=(tan t−cot t)/(tan t+cot t)
Replies
3
Views
2K
MHB Proving a trigonometric identity
Replies
7
Views
3K
MHB How to Prove the Trigonometric Inequality for Real Numbers?
Replies
6
Views
2K
MHB Can you prove this identity using trigonometric identities?
Replies
5
Views
2K
MHB Can Trigonometric Inequalities Be Proven with Simple Equations?
Replies
2
Views
1K
MHB Proving a trigonometric identity II
Replies
2
Views
2K
MHB Prove trig identity (cot x -1)/(cot x +1)=(1-sin 2x)/(cos 2x)
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top