MHB Stuck on a trigonometric identity proof....

AI Thread Summary
The discussion revolves around proving the trigonometric identity $\frac{1 -\cos A}{1 + \cos A} = (\cot A - \csc A)^2$. Participants suggest transforming the right side into sine and cosine terms for simplification. One user demonstrates a method by multiplying the left side by $\frac{1 - \cos A}{1 - \cos A}$ to facilitate the proof. Ultimately, the user expresses gratitude after successfully solving the problem. The exchange highlights collaborative problem-solving in trigonometric proofs.
Riwaj
Messages
12
Reaction score
0
$\frac{1 -\cos A}{1 + \cos A} = (\cot A - \csc A)^2$
 
Last edited by a moderator:
Mathematics news on Phys.org
Re: please prove it i am stuck ...

Riwaj said:
$\frac{1 -\cos A}{1 + \cos A} = (\cot A - \csc A)^2$
Hi Riwaj,

What did yo try so far ?
 
Re: please prove it i am stuck ...

My approach would be to change the cosecant and cotangent on the right side to sine and cosine, then do the indicated operations on the right.
 
Here's the start of another approach:

$$\frac{1 - \cos x}{1 + \cos x} \cdot \frac{1 - \cos x}{1 - \cos x} = \frac{1 - 2\cos x + \cos^2 x}{\sin^2 x}$$
 
oh ... thank you everyone i got it now
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
View full post »
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 '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
MHB Solve Situational Problems Involving Trigonometric Identities
Replies
3
Views
2K
MHB How to Prove a Trigonometric Identity Involving x, y, and z?
Replies
1
Views
1K
I Is this a Trigonometric Identity?
Replies
20
Views
2K
MHB Can you prove the following two difficult trigonometric identities?
Replies
3
Views
1K
I Question ,trigonometric identities equation and functions ?
Replies
4
Views
1K
MHB What is the Proof for the Trigonometric Sum Identity?
Replies
2
Views
1K
B What values of m as a function of q satisfy this trigonometric equation?
Replies
5
Views
1K
MHB Simple Trigonometric Identities
Replies
9
Views
2K

Hot Threads

Recent Insights

Back
Top