Expert: Sherman D. - 10/22/2004

Question
Hi Sherman:

Hope you can help.

Prove that:  

sin@ /1-cos@  -  1+ cos@ /sin@ = 0

I'm not sure how to find the commom denominator to do the  subtraction.

Is it posible to help with this. A friend of mine recommended you yesterday.

Thanks a million.

Answer
If by this you mean

(sinX/(1 - cosX)) - ((1 + cosX)/(sinX)) = 0

multiply everything by (1 - cosX)(sinX)

((sinX)^2 - ((1 + cosX)(1 - cosX)))/(sinX(1 - cosX))

((sinX)^2 - (1 - cosX + cosX - (cosX)^2)) / (sinX - sinXcosX)

((sinX)^2 - (1 - (cosX)^2)) / (sinX - sinXcosX)

Using the info at
www-physics.ucsd.edu/~aklohs/studies/math/trig.html

((sinX)^2 - 1 + (cosX)^2) / (sinX - sinXcosX)

((sinX)^2 + (cosX)^2 - 1)/(sinX - sinXcosX)

(((sinX)^2 + (cosX)^2) - 1)/(sinX - sinXcosX)

(1 - 1)/(sinX - sinXcosX)

0/(sinX - sinXcosX) = 0

so if by @ you mean "x", I think i just prooved that your problem is true.

at the site provided, you will see a problem that looks like this
sin² A + cos² A = 1

which is the same as
(sinX)^2 + (cosX)^2