Question

How do you rationalize the denominator for `sqrt((1-cosbeta)/(1+cosbeta))`?

Answer 1

Multiply and divide with `1-cosb` hence

#sqrt(((1-cosb)*(1-cosb))/((1+cosb)(1-cosb)))= sqrt(((1-cosb)^2)/(1-cos^2b))= sqrt(((1-cosb)^2)/((sin^2b)))= sqrt(((1-cosb)/sinb))^2= abs((1-cosb)/sinb)#