MHB How Do You Solve These Trigonometric Identities?

AI Thread Summary
The discussion centers on solving the trigonometric identity (2 - 5cot x) / (2 + 5cot x) = (2sin x - 5cos x) / (2sin x + 5cos x). Participants question the accuracy of the identity and suggest that it should instead be written with cotangent on both sides. Two methods for solving the identity are proposed: multiplying the left side by sin x/sin x or the right side by csc x/csc x. Additionally, the relationships between cotangent, cosecant, sine, and cosine are highlighted as essential for simplifying the expression. The conversation emphasizes the importance of correctly identifying and manipulating trigonometric identities.
fluffertoes
Messages
16
Reaction score
0
How do you do this one? I can't figure it out!
(2 - 5cot x) / (2 + 5cos x) = (2sin x - 5cos x) / (2sin x + 5cos x)
 
Mathematics news on Phys.org
Are you sure you've copied it correctly? It appears to me that the actual identity should be:

$$\frac{2-5\cot(x)}{2+5\cot(x)}=\frac{2\sin(x)-5\cos(x)}{2\sin(x)+5\cos(x)}$$
 
fluffertoes said:
How do you do this one? I can't figure it out!
(2 - 5cot x) / (2 + 5cot x) = (2sin x - 5cos x) / (2sin x + 5cos x)

fixedtwo ways to go

1) multiply left side by sinx/sinx

or

2) multiply right side by cscx/cscx

recall cotx = cosx/sinx and cscx = 1/sinx
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
Thread 'Imaginary Pythagorus'
I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
Back
Top