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Expert: Robi Bhattacharjee - 8/28/2008


Question
QUESTION: i have to prove how these two trig formulas are equal could you help?

(Cot(x)-1)/(Cot(x)+1) =  (1-Sin(2x))/Cos(x)

anything would be appreciated
Thanks!

Austin

ANSWER: Hello Austin,

Great question!!

I also had a hard time with this question. Now, I just realized something, this equation is not true. I tested some values and it doesn't work. Either you have typed it wrong, or this problem isn't an identity.






If its a typo please type it up again.



Happy to help,

Robi

---------- FOLLOW-UP ----------

QUESTION: i did have a typo on the end of the equasion its cos(2x) so the equasion would read


(Cot(x)-1)/(Cot(x)+1) =  (1-Sin(2x))/Cos(2x)  

Answer
Hi austin,

This seems about right and I have solved it.

Take the right side and start simplifying.

1- sin2x / cos 2x = (1 - 2sinxcosx) / (cosx^2 - sinx ^2)

I just used the formulas

so it = (sinx^2 - 2sinxcosx + cosx^2) / (cosx^2 - sinx^2) since sinx ^2

+ cosx ^ 2 = 1

so it = (cosx - sinx)^2 / (cosx - sinx)(cosx + sinx) by factoring

so canceling : it = (cosx - sinx) / (cosx + sinx) now dividing top and

bottom we get = (cotx - 1)/(cotx + 1)


Thats it,

Feel free to ask if you are not clear on anything,


Robi  

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Robi Bhattacharjee

Expertise

I can answer a variety of questions on mathematics. Questions on trigonometry, calculus(preferably single variable), algebra, geometry, and number theory will be answered. I cannot answer questions on abstract branches of mathematics such as group theory. I also cannot answer questions on statistics. In number theory, I can answer questions on congruences, prime numbers, units, functions, and the riemann-zeta function.

Experience

I have studied advanced math my entire life. I started calculus in sixth grade. I have attended numerous math competitions and I am attending math organizations such as the San-Diego math circle. Also, this year I have been invited to the USAMO which is a prestigious math competition (Every year the USAMO invites 500 students from across the USA to participate in this competition. The top 6 go to represent the USA in the International Math Olympiad).

Organizations
I am in the San Diego Math Circle

Education/Credentials
I am entering high school and have received a perfect score and the STAR test 5 times in a row. I also have gotten recognitions in the AMC 10, AIME, Math Counts, and ARML. Additionally, I have won the San Diego Math Olimpiad twice in a row.

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